Transmitting apparatus and bit interleaving method thereof

ABSTRACT

A transmitting apparatus is provided. The transmitting apparatus includes: an encoder configured to generate a low-density parity check (LDPC) codeword by LDPC encoding of input bits based on a parity check matrix including information word bits and parity bits, the LDPC codeword including a plurality of bit groups each including a plurality of bits; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the interleaver is further configured to interleave the LDPC codeword such that a bit included in a predetermined bit group from among the plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

CROSS-REFERENCE TO RELATED APPLICATION

This is a Continuation of U.S. application Ser. No. 17/060,682 filedOct. 1, 2020, which is a Continuation of U.S. application Ser. No.16/460,305 filed Jul. 2, 2019, which is a Continuation of U.S.application Ser. No. 15/686,280 filed Aug. 25, 2017, which is aContinuation of application Ser. No. 14/716,503 filed May 19, 2015, andclaims priority from U.S. Provisional Application No. 62/001,160 filedon May 21, 2014 and Korean Patent Application No. 10-2015-0069924 filedon May 19, 2015, the disclosures of which are incorporated herein byreference in their entirety.

BACKGROUND 1. Field

Apparatuses and methods consistent with exemplary embodiments relate toa transmitting apparatus and an interleaving method thereof, and moreparticularly, to a transmitting apparatus which processes and transmitsdata, and an interleaving method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcastingcommunication services are moving into the era of digitalization,multi-channel, wideband, and high quality. In particular, as highquality digital televisions, portable multimedia players and portablebroadcasting equipment are increasingly used in recent years, there isan increasing demand for methods for supporting various receivingmethods of digital broadcasting services.

In order to meet such demand, standard groups are establishing variousstandards and are providing a variety of services to satisfy users'needs. Therefore, there is a need for a method for providing improvedservices to users with high decoding and receiving performance.

SUMMARY

Exemplary embodiments of the inventive concept may overcome the abovedisadvantages and other disadvantages not described above. However, itis understood that the exemplary embodiment are not required to overcomethe disadvantages described above, and may not overcome any of theproblems described above.

The exemplary embodiments provide a transmitting apparatus which can mapa bit included in a predetermined bit group from among a plurality ofbit groups of a low density parity check (LDPC) codeword onto apredetermined bit of a modulation symbol, and transmit the bit, and aninterleaving method thereof.

According to an aspect of an exemplary embodiment, there is provided atransmitting apparatus including: an encoder configured to generate anLDPC codeword by LDPC encoding; an interleaver configured to interleavethe LDPC codeword; and a modulator configured to map the interleavedLDPC codeword onto a modulation symbol, wherein the modulator is furtherconfigured to map a bit included in a predetermined bit group from amonga plurality of bit groups constituting the LDPC codeword onto apredetermined bit of the modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits. Mmay be a common divisor of N_(ldpc) and K_(ldpc) and may be determinedto satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. In this case, Q_(ldpc) may bea cyclic shift parameter value regarding columns in a column group of aninformation word submatrix of a parity check matrix, N_(ldpc) may be alength of the LDPC codeword, and K_(ldpc) may be a length of informationword bits of the LDPC codeword.

The interleaver may include: a parity interleaver configured tointerleave parity bits of the LDPC codeword; a group interleaverconfigured to divide the parity-interleaved LDPC codeword by theplurality of bit groups and rearrange an order of the plurality of bitgroups in bit group wise; and a block interleaver configured tointerleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of theplurality of bit groups in bit group wise by using the followingequation:Y _(j) =X _(π(j)) (0≤j<N _(group)),where X_(j) is a j^(th) bit group before the plurality of bit groups areinterleaved, Y_(j) is a j^(th) bit group after the plurality of bitgroups are interleaved, N_(group) is a total number of the plurality ofbit groups, and π(j) is a parameter indicating an interleaving order.

Here, π(j) may be determined based on at least one of a length of theLDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method is16-QAM, and the code rate is 5/15, π(j) may be defined as in table 15.

The block interleaver may be configured to interleave by writing theplurality of bit groups in each of a plurality of columns in bit groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bit groupwise in a row direction.

The block interleaver may be configured to serially write, in theplurality of columns, at least some bit groups which are writable in theplurality of columns in bit group wise from among the plurality of bitgroups, and then divide and write the other bit groups in an area whichremains after the at least some bit groups are written in the pluralityof columns in bit group wise.

According to an aspect of another exemplary embodiment, there isprovided an interleaving method of a transmitting apparatus, including:generating an LDPC codeword by LDPC encoding; interleaving the LDPCcodeword; and mapping the interleaved LDPC codeword onto a modulationsymbol, wherein the mapping comprises mapping a bit included in apredetermined bit group from among a plurality of bit groupsconstituting the LDPC codeword onto a predetermined bit of themodulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc) and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. In this case,Q_(ldpc) may be a cyclic shift parameter value regarding columns in acolumn group of an information word submatrix of a parity check matrix,N_(ldpc) may be a length of the LDPC codeword, and K_(ldpc) may be alength of information word bits of the LDPC codeword.

The interleaving may include: interleaving parity bits of the LDPCcodeword; dividing the parity-interleaved LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise; and interleaving the plurality of bit groups the orderof which is rearranged.

The rearranging in bit group wise may include rearranging the order ofthe plurality of bit groups in bit group wise by using the followingequation:Y _(j) =X _(π(j)) (0≤j<N _(group)),where X_(j) is a j^(th) bit group before the plurality of bit groups areinterleaved, Y_(j) is a j^(th) bit group after the plurality of bitgroups are interleaved, N_(group) is a total number of the plurality ofbit groups, and π(j) is a parameter indicating an interleaving order.

Here, π(j) may be determined based on at least one of a length of theLDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method is16-QAM, and the code rate is 5/15, π(j) may be defined as in table 15.

The interleaving the plurality of bit groups may include interleaving bywriting the plurality of bit groups in each of a plurality of columns inbit group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbit group wise in a row direction.

The interleaving the plurality of bit groups may include seriallywriting, in the plurality of columns, at least some bit groups which arewritable in the plurality of columns in bit group wise from among theplurality of bit groups, and then dividing and writing the other bitgroups in an area which remains after the at least some bit groups arewritten in the plurality of columns in bit group wise.

According to various exemplary embodiments, improved decoding andreceiving performance can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing indetail exemplary embodiments, with reference to the accompanyingdrawings, in which:

FIGS. 1A to 12 are views to illustrate a transmitting apparatusaccording to exemplary embodiments;

FIGS. 13 to 18 are views to illustrate a receiving apparatus accordingto exemplary embodiments;

FIG. 19 is a block diagram to illustrate a configuration of atransmitting apparatus, according to an exemplary embodiment;

FIGS. 20 to 22 are views to illustrate a configuration of a parity checkmatrix, according to exemplary embodiments;

FIG. 23 is a block diagram to illustrate a configuration of aninterleaver, according to an exemplary embodiment;

FIGS. 24 to 26 are views to illustrate an interleaving method, accordingto exemplary embodiments;

FIGS. 27 to 32 are views to illustrate an interleaving operation of ablock interleaver, according to exemplary embodiments;

FIG. 33 is a view to illustrate an operation of a demultiplexer,according to an exemplary embodiment;

FIG. 34 is a view to illustrate a method for designing an interleavingpattern, according to exemplary embodiments;

FIG. 35 is a view to illustrate a configuration of a receiving apparatusaccording to an exemplary embodiment;

FIG. 36 is a view to illustrate a configuration of a deinterleaveraccording to an exemplary embodiment,

FIG. 37 is a view to illustrate a deinterleaving operation of a blockdeinterleaver, according to an exemplary embodiment;

FIG. 38 is a flowchart to illustrate an interleaving method, accordingto an exemplary embodiment;

FIG. 39 is a block diagram illustrating a configuration of a receivingapparatus according to an exemplary embodiment;

FIG. 40 is a block diagram illustrating a demodulator according to anexemplary embodiment; and

FIG. 41 is a flowchart provided to illustrate an operation of areceiving apparatus from a moment when a user selects a service untilthe selected service is reproduced, according to an exemplaryembodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greaterdetail with reference to the accompanying drawings.

In the following description, same reference numerals are used for thesame elements when they are depicted in different drawings. The mattersdefined in the description, such as detailed construction and elements,are provided to assist in a comprehensive understanding of the exemplaryembodiments. Thus, it is apparent that the exemplary embodiments can becarried out without those specifically defined matters. Also, functionsor elements known in the related art are not described in detail sincethey would obscure the exemplary embodiments with unnecessary detail.

FIG. 1A is provided to explain transmitting apparatus according to anexemplary embodiment.

According to FIG. 1A, a transmitting apparatus 10000 according to anexemplary embodiment may include an Input Formatting Block (or part)11000, 11000-1, a BIT Interleaved and Coded Modulation (BICM) block12000, 12000-1, a Framing/Interleaving block 13000, 13000-1 and aWaveform Generation block 14000, 14000-1.

The transmitting apparatus 10000 according to an exemplary embodimentillustrated in FIG. 1A includes normative blocks shown by solid linesand informative blocks shown by dotted lines. Here, the blocks shown bysolid lines are normal blocks, and the blocks shown by dotted lines areblocks which may be used when implementing an informative MIMO.

The Input Formatting block 11000, 11000-1 generates a baseband frame(BBFRAME) from an input stream of data to be serviced. Herein, the inputstream may be a transport stream (TS), Internet protocol (IP) stream, ageneric stream (GS), a generic stream encapsulation (GSE), etc.

The BICM block 12000, 12000-1 determines a forward error correction(FEC) coding rate and a constellation order depending on a region wherethe data to be serviced will be transmitted (e.g., a fixed PHY frame ormobile PHY frame), and then, performs encoding. Signaling information onthe data to be serviced may be encoded through a separate BICM encoder(not illustrated) or encoded by sharing the BICM encoder 12000, 12000-1with the data to be serviced, depending on a system implementation.

The Framing/Interleaving block 13000, 13000-1 combines time interleaveddata with signaling information to generate a transmission frame.

The Waveform Generation block 14000, 14000-1 generates an OFDM signal inthe time domain on the generated transmission frame, modulates thegenerated OFDM signal to a radio frequency (RF) signal and transmits themodulated RF signal to a receiver.

FIGS. 1B and 1C are provided to explain methods of multiplexingaccording to an exemplary embodiment.

FIG. 1B illustrates a block diagram to implement a Time DivisionMultiplexing according to an exemplary embodiment.

In the TDM system architecture, there are four main blocks (or parts):the Input Formatting block 11000, the BICM block 12000, theFraming/Interleaving block 13000, and the Waveform Generation block14000.

Data is input and formatted in the Input Formatting block, and forwarderror correction applied and mapped to constellations in the BICM block12000. Interleaving, both time and frequency, and frame creation done inthe Framing/Interleaving block 13000. Subsequently, the output waveformis created in the Waveform Generation block 14000.

FIG. 2B illustrates a block diagram to implement a Layered DivisionMultiplexing (LDM) according to another exemplary embodiment.

In the LDM system architecture, there are several different blockscompared with the TDM system architecture. Specifically, there are twoseparate Input Formatting blocks 11000, 11000-1 and BICM blocks 12000,12000-1, one for each of the layers in LDM. These are combined beforethe Framing/Interleaving block 13000 in the LDM Injection block. TheWaveform Generation block 14000 is similar to TDM.

FIG. 2 is a block diagram which illustrates detailed configuration ofthe Input Formatting block illustrated in FIG. 1A.

As illustrated in FIG. 2 , the Input Formatting block 11000 consists ofthree blocks which control packets distributed into PLPs. Specifically,the Input Formatting block 11000 includes a packet encapsulation andcompression block 11100, a baseband framing block 11200 and a schedulerblock 11300.

Input data packets input to the Input Formatting block 11000 can consistof various types, but at the encapsulation operation these differenttypes of packets become generic packets which configure baseband frames.Here, the format of generic packets is variable. It is possible toeasily extract the length of the generic packet from the packet itselfwithout additional information. The maximum length of the generic packetis 64 kB. The maximum length of the generic packet, including header, isfour bytes. Generic packets must be of integer byte length.

The scheduler 11200 receives an input stream of encapsulated genericpackets and forms them into physical layer pipes (PLPs), in the form ofbaseband frames. In the above-mentioned TDM system there may be only onePLP, called single PLP or S-PLP, or there may be multiple PLPs, calledM-PLP. One service cannot use more than four PLPs. In the case of an LDMsystem consisting of two layers, two PLPs are used, one for each layer.

The scheduler 11200 receives encapsulated input packet streams anddirects how these packets are allocated to physical layer resources.Specifically, the scheduler 11200 directs how the baseband framing blockwill output baseband frames.

The functional assets of the Scheduler 11200 are defined by data size(s)and time(s). The physical layer can deliver portions of data at thesediscrete times. The scheduler 11200 uses the inputs and informationincluding encapsulated data packets, quality of service metadata for theencapsulated data packets, a system buffer model, constraints andconfiguration from system management, and creates a conforming solutionin terms of configuration of the physical layer parameters. Thecorresponding solution is subject to the configuration and controlparameters and the aggregate spectrum available.

Meanwhile, the operation of the Scheduler 11200 is constrained bycombination of dynamic, quasi-static, and static configurations. Thedefinition of these constraints is left to implementation.

In addition, for each service a maximum of four PLPs shall be used.Multiple services consisting of multiple time interleaving blocks may beconstructed, up to a total maximum of 64 PLPs for bandwidths of 6, 7 or8 MHz. The baseband framing block 11300, as illustrated in FIG. 3A,consists of three blocks, baseband frame construction 3100, 3100-1, . .. 3100-n, baseband frame header construction block 3200, 3200-1, . . .3200-n, and the baseband frame scrambling block 3300, 3300-1, . . .3300-n. In a M-PLP operation, the baseband framing block createsmultiple PLPs as necessary.

A baseband frame 3500, as illustrated in FIG. 3B, consists of a basebandframe header 3500-1 and payload 3500-2 consisting of generic packets.Baseband frames have fixed length K_(payload). Generic packets 3610-3650shall be mapped to baseband frames 3500 in order. If generic packets3610-3650 do not completely fit within a baseband frame, packets aresplit between the current baseband frame and the next baseband frame.Packet splits shall be in byte units only.

The baseband frame header construction block 3200, 3200-1, . . . 3200-nconfigures the baseband frame header. The baseband frame header 3500-1,as illustrated in FIG. 3B, is composed of three parts, including thebase header 3710, the optional header (or option field 3720) and theextension field 3730. Here, the base header 3710 appears in everybaseband frame, and the optional header 3720 and the extension field3730 may not be present in every time.

The main feature of the base header 3710 is to provide a pointerincluding an offset value in bytes as an initiation of the next genericpacket within the baseband frame. When the generic packet initiates thebaseband frame, the pointer value becomes zero. If there is no genericpacket which is initiated within the baseband frame, the pointer valueis 8191, and a 2-byte base header may be used.

The extension field (or extension header) 3730 may be used later, forexample, for the baseband frame packet counter, baseband frame timestamping, and additional signaling, etc.

The baseband frame scrambling block 3300, 3300-1, . . . 3300-n scramblesthe baseband frame.

In order to ensure that the payload data when mapped to constellationsdoes not always map to the same point, such as when the payload mappedto constellations consists of a repetitive sequence, the payload datashall always be scrambled before forward error correction encoding.

The scrambling sequences shall be generated by a 16-bit shift registerthat has 9 feedback taps. Eight of the shift register outputs areselected as a fixed randomizing byte, where each bit from t his byte isused to individually XOR the corresponding input data. The data bits areXORed MSB to MSB and so on until LSB to LSB. The generator polynomial isG(x)=1+X+X³+X⁶+X⁷+X¹¹+X¹²+X¹³+X¹⁶.

FIG. 4 illustrates a shift register of a PRBS encoder for scrambling abaseband according to an exemplary embodiment, wherein loading of thesequence into the PRBS register, as illustrated in FIG. 4 and shall beinitiated at the start of every baseband frame.

FIG. 5 is a block diagram provided to explain detailed configuration ofthe BICM block illustrated in FIG. 1A.

As illustrated in FIG. 5 , the BICM block includes the FEC block 14100,14100-1, . . . , 14100-n, Bit Interleaver block 14200, 14200-1, . . . ,14200-n and Mapper blocks 14300, 14300-1, . . . , 14300-n.

The input to the FEC block 1400, 14100-1, . . . , 14100-n is a Basebandframe, of length K_(payload), and the output from the FEC block is a FECframe. The FEC block 14100, 14100-1, . . . , 14100-n is implemented byconcatenation of an outer code and an inner code with the informationpart. The FEC frame has length N_(inner). There are two differentlengths of LDPC code defined: N_(inner)=64800 bits and N_(inner)=16200bits

The outer code is realized as one of either Bose, Ray-Chaudhuri andHocquenghem (BCH) outer code, a Cyclic Redundancy Check (CRC) or othercode. The inner code is realized as a Low Density Parity Check (LDPC)code. Both BCH and LDPC FEC codes are systematic codes where theinformation part I contained within the codeword. The resulting codewordis thus a concatenation of information or payload part, BCH or CRCparities and LDPC parities, as shown in FIG. 6A.

The use of LDPC code is mandatory and is used to provide the redundancyneeded for the code detection. There are two different LDPC structuresthat are defined, these are called Type A and Type B. Type A has a codestructure that shows better performance at low code rates while Type Bcode structure shows better performance at high code rates. In generalN_(inner)=64800 bit codes are expected to be employed. However, forapplications where latency is critical, or a simpler encoder/decoderstructure is preferred, N_(inner)=16200 bit codes may also be used.

The outer code and CRC consist of adding M_(outer) bits to the inputbaseband frame. The outer BCH code is used to lower the inherent LDPCerror floor by correcting a predefined number of bit errors. When usingBCH codes the length of M_(outer) is 192 bits (N_(inner)64800 bit codes)and 168 bits (for N_(inner)=16200 bit codes). When using CRC the lengthof M_(outer) is 32 bits. When neither BCH nor CRC are used the length ofM_(outer) is zero. The outer code may be omitted if it is determinedthat the error correcting capability of the inner code is sufficient forthe application. When there is no outer code the structure of the FECframe is as shown in FIG. 6B.

FIG. 7 is a block diagram provided to explain detailed configuration ofthe Bit Interleaver block illustrated in FIG. 6 .

The LDPC codeword of the LDPC encoder, i.e., a FEC Frame, shall be bitinterleaved by a Bit Interleaver block 14200. The Bit Interleaver block14200 includes a parity interleaver 14210, a group-wise interleaver14220 and a block interleaver 14230. Here, the parity interleaver is notused for Type A and is only used for Type B codes.

The parity interleaver 14210 converts the staircase structure of theparity-part of the LDPC parity-check matrix into a quasi-cyclicstructure similar to the information-part of the matrix.

Meanwhile, the parity interleaved LDPC coded bits are split intoN_(group)=N_(inner)/360 bit groups, and the group-wise interleaver 14220rearranges the bit groups.

The block interleaver 14230 block interleaves the group-wise interleavedLDPC codeword.

Specifically, the block interleaver 14230 divides a plurality of columnsinto part 1 and part 2 based on the number of columns of the blockinterleaver 14230 and the number of bits of the bit groups. In addition,the block interleaver 14230 writes the bits into each column configuringpart 1 column wise, and subsequently writes the bits into each columnconfiguring part 2 column wise, and then reads out row wise the bitswritten in each column.

In this case, the bits constituting the bit groups in the part 1 may bewritten into the same column, and the bits constituting the bit groupsin the part 2 may be written into at least two columns.

Back to FIG. 5 , the Mapper block 14300, 14300-1, . . . , 14300-n mapsFEC encoded and bit interleaved bits to complex valued quadratureamplitude modulation (QAM) constellation points. For the highestrobustness level, quaternary phase shift keying (QPSK) is used. Forhigher order constellations (16-QAM up to 4096-QAM), non-uniformconstellations are defined and the constellations are customized foreach code rate.

Each FEC frame shall be mapped to a FEC block by first de-multiplexingthe input bits into parallel data cell words and then mapping these cellwords into constellation values.

FIG. 8 is a block diagram provided to explain detailed configuration ofa Framing/Interleaving block illustrated in FIG. 1A.

As illustrated in FIG. 8 , the Framing/Interleaving block 14300 includesa time interleaving block 14310, a framing block 14320 and a frequencyinterleaving block 14330.

The input to the time interleaving block 14310 and the framing block14320 may consist of M-PLPs however the output of the framing block14320 is OFDM symbols, which are arranged in frames. The frequencyinterleaver included in the frequency interleaving block 14330 operatesan OFDM symbols.

The time interleaver (TI) configuration included in the timeinterleaving block 14310 depends on the number of PLPs used. When thereis only a single PLP or when LDM is used, a sheer convolutionalinterleaver is used, while for multiple PLP a hybrid interleaverconsisting of a cell interleaver, a block interleaver and aconvolutional interleaver is used. The input to the time interleavingblock 14310 is a stream of cells output from the mapper block (FIG. 5,14300, 14300-1 , . . . , 14300-n), and the output of the timeinterleaving block 14310 is also a stream of time-interleaved cells.

FIG. 9A illustrates the time interleaving block for a single PLP(S-PLP), and it consists of a convolutional interleaver only.

FIG. 9B illustrates the time interleaving block for a plurality of PLPs(M-PLP), and it can be divided in several sub-blocks as illustrated.

The framing block 14320 maps the interleaved frames onto at least onetransmitter frame. The framing block 14320, specifically, receivesinputs (e.g. data cell) from at least one physical layer pipes andoutputs symbols.

In addition, the framing block 14320 creates at least one special symbolknown as preamble symbols. These symbols undergo the same processing inthe waveform block mentioned later.

FIG. 10 is a view illustrating an example of a transmission frameaccording to an exemplary embodiment.

As illustrated in FIG. 10 , the transmission frame consists of threeparts, the bootstrap, preamble and data payload. Each of the three partsconsists of at least one symbol.

Meanwhile, the purpose of the frequency interleaving block 14330 is toensure that sustained interference in one part of the spectrum will notdegrade the performance of a particular PLP disproportionately comparedto other PLPs. The frequency interleaver 14330, operating on the all thedata cells of one OFDM symbol, maps the data cells from the framingblock 14320 onto the N data carriers.

FIG. 11 is a block diagram provided to explain detailed configuration ofa Waveform Generation block illustrated in FIG. 1A.

As illustrated in FIG. 11 , the Waveform Generation block 14000 includesa pilot inserting block 14100, a MISO block 14200, an IFFT block 14300,a PAPR block 14400, a GI inserting block 14500 and a bootstrap block14600.

The pilot inserting block 14100 inserts a pilot to various cells withinthe OFDM frame.

Various cells within the OFDM frame are modulated with referenceinformation whose transmitted value is known to the receiver.

Cells containing the reference information are transmitted at a boostedpower level. The cells are called scattered, continual, edge, preambleor frame-closing pilot cells. The value of the pilot information isderived from a reference sequence, which is a series of values, one foreach transmitted carrier on any given symbol.

The pilots can be used for frame synchronization, frequencysynchronization, time synchronization, channel estimation, transmissionmode identification and can also be used to follow the phase noise.

The pilots are modulated according to reference information, and thereference sequence is applied to all the pilots (e.g. scattered,continual edge, preamble and frame closing pilots) in every symbolincluding preamble and the frame-closing symbol of the frame.

The reference information, taken from the reference sequence, istransmitted in scattered pilot cells in every symbol except the preambleand the frame-closing symbol of the frame.

In addition to the scattered pilots described above, a number ofcontinual pilots are inserted in every symbol of the frame except forPreamble and the frame-closing symbol. The number and location ofcontinual pilots depends on both the FFT size and scattered pilotpattern in use.

The MISO block 14200 applies a MISO processing.

The Transmit Diversity Code Filter Set is a MISO pre-distortiontechnique that artificially decorrelates signals from multipletransmitters in a Single Frequency Network in order to minimizepotential destructive interference. Linear frequency domain filters areused so that the compensation in the receiver can be implemented as partof the equalizer process. The filter design is based on creatingall-pass filters with minimized cross-correlation over all filter pairsunder the constraints of the number of transmitters M∈{2,3,4} and thetime domain span of the filters N∈{64,256}. The longer time domain spanfilters will increase the decorrelation level, but the effective guardinterval length will be decreased by the filter time domain span andthis should be taken into consideration when choosing a filter set for aparticular network topology.

The IFFT block 14300 specifies the OFDM structure to use for eachtransmission mode. The transmitted signal is organized in frames. Eachframe has a duration of T_(F), and consists of L_(F) OFDM symbols. Nframes constitute one super-frame. Each symbol is constituted by a setof K_(total) carriers transmitted with a duration T_(S). Each symbol iscomposed of a useful part with duration T_(U) and a guard interval witha duration Δ. The guard interval consists of a cyclic continuation ofthe useful part, T_(U), and is inserted before it.

The PAPR block 14400 applies the Peak to Average Power Reductiontechnique.

The GI inserting block 14500 inserts the guard interval into each frame.

The bootstrap block 14600 prefixes the bootstrap signal to the front ofeach frame.

FIG. 12 is a block diagram provided to explain a configuration ofsignaling information according to an exemplary embodiment.

The input processing block 11000 includes a scheduler 11200. The BICMblock 15000 includes an L1 signaling generator 15100, an FEC encoder15200-1 and 15200-2, a bit interleaver 15300-2, a demux 15400-2,constellation mappers 15500-1 and 15500-2. The L1 signaling generator15100 may be included in the input processing block 11000, according toan exemplary embodiment.

An n number of service data are mapped to a PLP0 to a PLPn respectively.The scheduler 11200 determines a position, modulation and coding ratefor each PLP in order to map a plurality of PLPs to a physical layer ofT2. In other words, the scheduler 11200 generates L1 signalinginformation. The scheduler 11200 may output dynamic field informationamong L1 post signaling information of a current frame, using theframing/Interleavingblock 13000 (FIG. 1 ) which may be referred to as aframe builder. Further, the scheduler 11200 may transmit the L1signaling information to the BICM block 15000. The L1 signalinginformation includes L1 pre signaling information and L1 post signalinginformation.

The L1 signaling generator 15100 may differentiate the L1 pre signalinginformation from the L1 post signaling information to output them. TheFEC encoders 15200-1 and 15200-2 perform respective encoding operationswhich include shortening and puncturing for the L1 pre signalinginformation and the L1 post signaling information. The bit interleaver15300-2 performs interleaving by bit for the encoded L1 post signalinginformation. The demux 15400-2 controls robustness of bits by modifyingan order of bits constituting cells and outputs the cells which includebits. Two constellation mappers 15500-1 and 15500-2 map the L1 presignaling information and the L1 post signaling information toconstellations, respectively. The L1 pre signaling information and theL1 post signaling information processed through the above describedprocesses are output to be included in each frame by theFraming/Interleaving block 13000 (FIG. 1 ).

FIG. 13 illustrates a structure of an receiving apparatus according toan embodiment of the present invention.

The apparatus 20000 for receiving broadcast signals according to anembodiment of the present invention can correspond to the apparatus10000 for transmitting broadcast signals, described with reference toFIG. 1 . The apparatus 20000 for receiving broadcast signals accordingto an embodiment of the present invention can include a synchronization& demodulation module 21000, a frame parsing module 22000, a demapping &decoding module 23000, an output processor 24000 and a signalingdecoding module 25000. A description will be given of operation of eachmodule of the apparatus 20000 for receiving broadcast signals.

The synchronization & demodulation module 21000 can receive inputsignals through m Rx antennas, perform signal detection andsynchronization with respect to a system corresponding to the apparatus20000 for receiving broadcast signals and carry out demodulationcorresponding to a reverse procedure of the procedure performed by theapparatus 10000 for transmitting broadcast signals.

The frame parsing module 22000 can parse input signal frames and extractdata through which a service selected by a user is transmitted. If theapparatus 10000 for transmitting broadcast signals performsinterleaving, the frame parsing module 22000 can carry outdeinterleaving corresponding to a reverse procedure of interleaving. Inthis case, the positions of a signal and data that need to be extractedcan be obtained by decoding data output from the signaling decodingmodule 25200 to restore scheduling information generated by theapparatus 10000 for transmitting broadcast signals.

The demapping & decoding module 23000 can convert the input signals intobit domain data and then deinterleave the same as necessary. Thedemapping & decoding module 23000 can perform demapping for mappingapplied for transmission efficiency and correct an error generated on atransmission channel through decoding. In this case, the demapping &decoding module 23000 can obtain transmission parameters necessary fordemapping and decoding by decoding the data output from the signalingdecoding module 25000.

The output processor 24000 can perform reverse procedures of variouscompression/signal processing procedures which are applied by theapparatus 10000 for transmitting broadcast signals to improvetransmission efficiency. In this case, the output processor 24000 canacquire necessary control information from data output from thesignaling decoding module 25000. The output of the output processor24000 corresponds to a signal input to the apparatus 10000 fortransmitting broadcast signals and may be MPEG-TSs, IP streams (v4 orv6) and generic streams.

The signaling decoding module 25000 can obtain PLS information from thesignal demodulated by the synchronization & demodulation module 21000.As described above, the frame parsing module 22000, demapping & decodingmodule 23000 and output processor 24000 can execute functions thereofusing the data output from the signaling decoding module 25000.

FIG. 14 illustrates a synchronization & demodulation module according toan embodiment of the present invention.

As shown in FIG. 14 , the synchronization & demodulation module 21000according to an embodiment of the present invention corresponds to asynchronization & demodulation module of an apparatus 20000 forreceiving broadcast signals using m Rx antennas and can include mprocessing blocks for demodulating signals respectively input through mpaths. The m processing blocks can perform the same processingprocedure. A description will be given of operation of the firstprocessing block 21000 from among the m processing blocks.

The first processing block 21000 can include a tuner 21100, an ADC block21200, a preamble detector 21300, a guard sequence detector 21400, awaveform transform block 21500, a time/frequency synchronization block21600, a reference signal detector 21700, a channel equalizer 21800 andan inverse waveform transform block 21900.

The tuner 21100 can select a desired frequency band, compensate for themagnitude of a received signal and output the compensated signal to theADC block 21200.

The ADC block 21200 can convert the signal output from the tuner 21100into a digital signal.

The preamble detector 21300 can detect a preamble (or preamble signal orpreamble symbol) in order to check whether or not the digital signal isa signal of the system corresponding to the apparatus 20000 forreceiving broadcast signals. In this case, the preamble detector 21300can decode basic transmission parameters received through the preamble.

The guard sequence detector 21400 can detect a guard sequence in thedigital signal. The time/frequency synchronization block 21600 canperform time/frequency synchronization using the detected guard sequenceand the channel equalizer 21800 can estimate a channel through areceived/restored sequence using the detected guard sequence.

The waveform transform block 21500 can perform a reverse operation ofinverse waveform transform when the apparatus 10000 for transmittingbroadcast signals has performed inverse waveform transform. When thebroadcast transmission/reception system according to one embodiment ofthe present invention is a multi-carrier system, the waveform transformblock 21500 can perform FFT. Furthermore, when the broadcasttransmission/reception system according to an embodiment of the presentinvention is a single carrier system, the waveform transform block 21500may not be used if a received time domain signal is processed in thefrequency domain or processed in the time domain.

The time/frequency synchronization block 21600 can receive output dataof the preamble detector 21300, guard sequence detector 21400 andreference signal detector 21700 and perform time synchronization andcarrier frequency synchronization including guard sequence detection andblock window positioning on a detected signal. Here, the time/frequencysynchronization block 21600 can feed back the output signal of thewaveform transform block 21500 for frequency synchronization.

The reference signal detector 21700 can detect a received referencesignal. Accordingly, the apparatus 20000 for receiving broadcast signalsaccording to an embodiment of the present invention can performsynchronization or channel estimation.

The channel equalizer 21800 can estimate a transmission channel fromeach Tx antenna to each Rx antenna from the guard sequence or referencesignal and perform channel equalization for received data using theestimated channel.

The inverse waveform transform block 21900 may restore the originalreceived data domain when the waveform transform block 21500 performswaveform transform for efficient synchronization and channelestimation/equalization. If the broadcast transmission/reception systemaccording to an embodiment of the present invention is a single carriersystem, the waveform transform block 21500 can perform FFT in order tocarry out synchronization/channel estimation/equalization in thefrequency domain and the inverse waveform transform block 21900 canperform IFFT on the channel-equalized signal to restore transmitted datasymbols. If the broadcast transmission/reception system according to anembodiment of the present invention is a multi-carrier system, theinverse waveform transform block 21900 may not be used.

The above-described blocks may be omitted or replaced by blocks havingsimilar or identical functions according to design.

FIG. 15 illustrates a frame parsing module according to an embodiment ofthe present invention.

As shown in FIG. 15 , the frame parsing module 22000 according to anembodiment of the present invention can include at least one blockinterleaver 22100 and at least one cell demapper 22200.

The block interleaver 22100 can deinterleave data input through datapaths of the m Rx antennas and processed by the synchronization &demodulation module 21000 on a signal block basis. In this case, if theapparatus 10000 for transmitting broadcast signals performs pair-wiseinterleaving, the block interleaver 22100 can process two consecutivepieces of data as a pair for each input path. Accordingly, the blockinterleaver 22100 can output two consecutive pieces of data even whendeinterleaving has been performed. Furthermore, the block interleaver22100 can perform a reverse operation of the interleaving operationperformed by the apparatus 10000 for transmitting broadcast signals tooutput data in the original order.

The cell demapper 22200 can extract cells corresponding to common data,cells corresponding to data pipes and cells corresponding to PLS datafrom received signal frames. The cell demapper 22200 can merge datadistributed and transmitted and output the same as a stream asnecessary. When two consecutive pieces of cell input data are processedas a pair and mapped in the apparatus 10000 for transmitting broadcastsignals, the cell demapper 22200 can perform pair-wise cell demappingfor processing two consecutive input cells as one unit as a reverseprocedure of the mapping operation of the apparatus 10000 fortransmitting broadcast signals.

In addition, the cell demapper 22200 can extract PLS signaling datareceived through the current frame as PLS-pre & PLS-post data and outputthe PLS-pre & PLS-post data.

The above-described blocks may be omitted or replaced by blocks havingsimilar or identical functions according to design.

FIG. 16 illustrates a demapping & decoding module according to anembodiment of the present invention.

The demapping & decoding module 23000 shown in FIG. 16 can perform areverse operation of the operation of the bit interleaved and coded &modulation module illustrated in FIG. 1 .

The bit interleaved and coded & modulation module of the apparatus 10000for transmitting broadcast signals according to an embodiment of thepresent invention can process input data pipes by independently applyingSISO, MISO and MIMO thereto for respective paths, as described above.Accordingly, the demapping & decoding module 23000 illustrated in FIG.16 can include blocks for processing data output from the frame parsingmodule according to SISO, MISO and MIMO in response to the apparatus10000 for transmitting broadcast signals.

As shown in FIG. 16 , the demapping & decoding module 23000 according toan embodiment of the present invention can include a first block 23100for SISO, a second block 23200 for MISO, a third block 23300 for MIMOand a fourth block 23400 for processing the PLS-pre/PLS-postinformation. The demapping & decoding module 23000 shown in FIG. 16 isexemplary and may include only the first block 23100 and the fourthblock 23400, only the second block 23200 and the fourth block 23400 oronly the third block 23300 and the fourth block 23400 according todesign. That is, the demapping & decoding module 23000 can includeblocks for processing data pipes equally or differently according todesign.

A description will be given of each block of the demapping & decodingmodule 23000.

The first block 23100 processes an input data pipe according to SISO andcan include a time deinterleaver block 23110, a cell deinterleaver block23120, a constellation demapper block 23130, a cell-to-bit mux block23140, a bit deinterleaver block 23150 and an FEC decoder block 23160.

The time deinterleaver block 23110 can perform a reverse process of theprocess performed by the time interleaving block 14310 illustrated inFIG. 8 . That is, the time deinterleaver block 23110 can deinterleaveinput symbols interleaved in the time domain into original positionsthereof.

The cell deinterleaver block 23120 can perform a reverse process of theprocess performed by the cell interleaver block illustrated in FIG. 9 a. That is, the cell deinterleaver block 23120 can deinterleave positionsof cells spread in one FEC block into original positions thereof. Thecell deinterleaver block 23120 may be omitted.

The constellation demapper block 23130 can perform a reverse process ofthe process performed by the mapper 12300 illustrated in FIG. 5 . Thatis, the constellation demapper block 23130 can demap a symbol domaininput signal to bit domain data. In addition, the constellation demapperblock 23130 may perform hard decision and output decided bit data.Furthermore, the constellation demapper block 23130 may output alog-likelihood ratio (LLR) of each bit, which corresponds to a softdecision value or probability value. If the apparatus 10000 fortransmitting broadcast signals applies a rotated constellation in orderto obtain additional diversity gain, the constellation demapper block23130 can perform 2-dimensional LLR demapping corresponding to therotated constellation. Here, the constellation demapper block 23130 cancalculate the LLR such that a delay applied by the apparatus 10000 fortransmitting broadcast signals to the I or Q component can becompensated.

The cell-to-bit mux block 23140 can perform a reverse process of theprocess performed by the mapper 12300 illustrated in FIG. 5 . That is,the cell-to-bit mux block 23140 can restore bit data mapped to theoriginal bit streams.

The bit deinterleaver block 23150 can perform a reverse process of theprocess performed by the bit interleaver 12200 illustrated in FIG. 5 .That is, the bit deinterleaver block 23150 can deinterleave the bitstreams output from the cell-to-bit mux block 23140 in the originalorder.

The FEC decoder block 23460 can perform a reverse process of the processperformed by the FEC encoder 12100 illustrated in FIG. 5 . That is, theFEC decoder block 23460 can correct an error generated on a transmissionchannel by performing LDPC decoding and BCH decoding.

The second block 23200 processes an input data pipe according to MISOand can include the time deinterleaver block, cell deinterleaver block,constellation demapper block, cell-to-bit mux block, bit deinterleaverblock and FEC decoder block in the same manner as the first block 23100,as shown in FIG. 16 . However, the second block 23200 is distinguishedfrom the first block 23100 in that the second block 23200 furtherincludes a MISO decoding block 23210. The second block 23200 performsthe same procedure including time deinterleaving operation to outputtingoperation as the first block 23100 and thus description of thecorresponding blocks is omitted.

The MISO decoding block 11110 can perform a reverse operation of theoperation of the MISO processing in the apparatus 10000 for transmittingbroadcast signals. If the broadcast transmission/reception systemaccording to an embodiment of the present invention uses STBC, the MISOdecoding block 11110 can perform Alamouti decoding.

The third block 23300 processes an input data pipe according to MIMO andcan include the time deinterleaver block, cell deinterleaver block,constellation demapper block, cell-to-bit mux block, bit deinterleaverblock and FEC decoder block in the same manner as the second block23200, as shown in FIG. 16 . However, the third block 23300 isdistinguished from the second block 23200 in that the third block 23300further includes a MIMO decoding block 23310. The basic roles of thetime deinterleaver block, cell deinterleaver block, constellationdemapper block, cell-to-bit mux block and bit deinterleaver blockincluded in the third block 23300 are identical to those of thecorresponding blocks included in the first and second blocks 23100 and23200 although functions thereof may be different from the first andsecond blocks 23100 and 23200.

The MIMO decoding block 23310 can receive output data of the celldeinterleaver for input signals of the m Rx antennas and perform MIMOdecoding as a reverse operation of the operation of the MIMO processingin the apparatus 10000 for transmitting broadcast signals. The MIMOdecoding block 23310 can perform maximum likelihood decoding to obtainoptimal decoding performance or carry out sphere decoding with reducedcomplexity. Otherwise, the MIMO decoding block 23310 can achieveimproved decoding performance by performing MMSE detection or carryingout iterative decoding with MMSE detection.

The fourth block 23400 processes the PLS-pre/PLS-post information andcan perform SISO or MISO decoding.

The basic roles of the time deinterleaver block, cell deinterleaverblock, constellation demapper block, cell-to-bit mux block and bitdeinterleaver block included in the fourth block 23400 are identical tothose of the corresponding blocks of the first, second and third blocks23100, 23200 and 23300 although functions thereof may be different fromthe first, second and third blocks 23100, 23200 and 23300.

The shortened/punctured FEC decoder 23410 can perform de-shortening andde-puncturing on data shortened/punctured according to PLS data lengthand then carry out FEC decoding thereon. In this case, the FEC decoderused for data pipes can also be used for PLS. Accordingly, additionalFEC decoder hardware for the PLS only is not needed and thus systemdesign is simplified and efficient coding is achieved.

The above-described blocks may be omitted or replaced by blocks havingsimilar or identical functions according to design.

The demapping & decoding module according to an embodiment of thepresent invention can output data pipes and PLS information processedfor the respective paths to the output processor, as illustrated in FIG.16 .

FIGS. 17 and 18 illustrate output processors according to embodiments ofthe present invention.

FIG. 17 illustrates an output processor 24000 according to an embodimentof the present invention. The output processor 24000 illustrated in FIG.17 receives a single data pipe output from the demapping & decodingmodule and outputs a single output stream.

The output processor 24000 shown in FIG. 17 can include a BB scramblerblock 24100, a padding removal block 24200, a CRC-8 decoder block 24300and a BB frame processor block 24400.

The BB scrambler block 24100 can descramble an input bit stream bygenerating the same PRBS as that used in the apparatus for transmittingbroadcast signals for the input bit stream and carrying out an XORoperation on the PRBS and the bit stream.

The padding removal block 24200 can remove padding bits inserted by theapparatus for transmitting broadcast signals as necessary.

The CRC-8 decoder block 24300 can check a block error by performing CRCdecoding on the bit stream received from the padding removal block24200.

The BB frame processor block 24400 can decode information transmittedthrough a BB frame header and restore MPEG-TSs, IP streams (v4 or v6) orgeneric streams using the decoded information.

The above-described blocks may be omitted or replaced by blocks havingsimilar or identical functions according to design.

FIG. 18 illustrates an output processor according to another embodimentof the present invention. The output processor 24000 shown in FIG. 18receives multiple data pipes output from the demapping & decodingmodule. Decoding multiple data pipes can include a process of mergingcommon data commonly applicable to a plurality of data pipes and datapipes related thereto and decoding the same or a process ofsimultaneously decoding a plurality of services or service components(including a scalable video service) by the apparatus for receivingbroadcast signals.

The output processor 24000 shown in FIG. 18 can include a BB descramblerblock, a padding removal block, a CRC-8 decoder block and a BB frameprocessor block as the output processor illustrated in FIG. 17 . Thebasic roles of these blocks correspond to those of the blocks describedwith reference to FIG. 17 although operations thereof may differ fromthose of the blocks illustrated in FIG. 17 .

A de-jitter buffer block 24500 included in the output processor shown inFIG. 18 can compensate for a delay, inserted by the apparatus fortransmitting broadcast signals for synchronization of multiple datapipes, according to a restored TTO (time to output) parameter.

A null packet insertion block 24600 can restore a null packet removedfrom a stream with reference to a restored DNP (deleted null packet) andoutput common data.

A TS clock regeneration block 24700 can restore time synchronization ofoutput packets based on ISCR (input stream time reference) information.

A TS recombining block 24800 can recombine the common data and datapipes related thereto, output from the null packet insertion block24600, to restore the original MPEG-TSs, IP streams (v4 or v6) orgeneric streams. The TTO, DNT and ISCR information can be obtainedthrough the BB frame header.

An in-band signaling decoding block 24900 can decode and output in-bandphysical layer signaling information transmitted through a padding bitfield in each FEC frame of a data pipe.

The output processor shown in FIG. 18 can BB-descramble the PLS-preinformation and PLS-post information respectively input through aPLS-pre path and a PLS-post path and decode the descrambled data torestore the original PLS data. The restored PLS data is delivered to asystem controller included in the apparatus for receiving broadcastsignals. The system controller can provide parameters necessary for thesynchronization & demodulation module, frame parsing module, demapping &decoding module and output processor module of the apparatus forreceiving broadcast signals.

The above-described blocks may be omitted or replaced by blocks havingsimilar r identical functions according to design.

FIG. 19 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment. Referringto FIG. 19 , the transmitting apparatus 100 includes an encoder 110, aninterleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a low density parity check (LDPC) codeword byperforming LDPC encoding based on a parity check matrix. To achievethis, the encoder 110 may include an LDPC encoder (not shown) to performthe LDPC encoding.

Specifically, the encoder 110 LDPC-encodes information word (orinformation) bits to generate the LDPC codeword which is formed ofinformation word bits and parity bits (that is, LDPC parity bits). Here,bits input to the encoder 110 may be used as the information word bits.Also, since an LDPC code is a systematic code, the information word bitsmay be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the paritybits. For example, the LDPC codeword is formed of N_(ldpc) number ofbits, and includes K_(ldpc) number of information word bits andN_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword byperforming the LDPC encoding based on the parity check matrix. That is,since the LDPC encoding is a process for generating an LDPC codeword tosatisfy H·C^(T)=0, the encoder 110 may use the parity check matrix whenperforming the LDPC encoding. Herein, H is a parity check matrix and Cis an LDPC codeword.

For the LDPC encoding, the transmitting apparatus 100 may include amemory and may pre-store parity check matrices of various formats.

For example, the transmitting apparatus 100 may pre-store parity checkmatrices which are defined in Digital Video Broadcasting-Cable version 2(DVB-C2), Digital Video Broadcasting-Satellite-Second Generation(DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial(DVB-T2), etc., or may pre-store parity check matrices which are definedin the North America digital broadcasting standard system AdvancedTelevision System Committee (ATSC) 3.0 standards, which are currentlybeing established. However, this is merely an example and thetransmitting apparatus 100 may pre-store parity check matrices of otherformats in addition to these parity check matrices.

Hereinafter, a parity check matrix according to various exemplaryembodiments will be explained in detail with reference to the drawings.In the parity check matrix, elements other than elements having 1 have0.

For example, the parity check matrix according to an exemplaryembodiment may have a configuration of FIG. 20 .

Referring to FIG. 20 , a parity check matrix 200 is formed of aninformation word submatrix (or an information submatrix) 210corresponding to information word bits, and a parity submatrix 220corresponding to parity bits.

The information word submatrix 210 includes K_(ldpc) number of columnsand the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc)number of columns. The number of rows of the parity check matrix 200 isidentical to the number of columns of the parity submatrix 220,N_(parity)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of anLDPC codeword, K_(ldpc) is a length of information word bits, andN_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length ofthe LDPC codeword, the information word bits, and the parity bits meanthe number of bits included in each of the LDPC codeword, theinformation word bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 andthe parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns(that is, 0^(th) column to (K_(ldpc)−1)^(th) column), and follows thefollowing rules:

First, M number of columns from among K_(ldpc) number of columns of theinformation word submatrix 210 belong to the same group, and K_(ldpc)number of columns is divided into K_(ldpc)/M number of column groups. Ineach column group, a column is cyclic-shifted from an immediatelyprevious column by Q_(ldpc). That is, Q_(ldpc) may be a cyclic shiftparameter value regarding columns in a column group of the informationword submatrix 210 of the parity check matrix 200.

Herein, M is an interval at which a pattern of a column group, whichincludes a plurality of columns, is repeated in the information wordsubmatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one columnis cyclic-shifted from an immediately previous column in a same columngroup in the information word submatrix 210. Also, M is a common divisorof N_(ldpc) and K_(ldpc) and is determined to satisfyQ_(ldpc)=(N_(ldpc)−K_(ldpc))/M Here, M and Q_(ldpc) are integers andK_(ldpc)/M is also an integer. M and Q_(ldpc) may have various valuesaccording to a length of the LDPC codeword and a code rate (CR)(or,coding rate).

For example, when M=360 and the length of the LDPC codeword, N_(ldpc),is 64800, Q_(ldpc) may be defined as in table 1 presented below, and,when M=360 and the length N_(ldpc) of the LDPC codeword is 16200,Q_(ldpc) may be defined as in table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc)  5/15 64800 360 120  6/15 64800360 108  7/15 64800 360 96  8/15 64800 360 84  9/15 64800 360 72 10/1564800 360 60 11/15 64800 360 48 12/15 64800 360 36 13/15 64800 360 24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc)  5/15 16200 360 30  6/15 16200 36027  7/15 16200 360 24  8/15 16200 360 21  9/15 16200 360 18 10/15 16200360 15 11/15 16200 360 12 12/15 16200 360 9 13/15 16200 360 6

Second, when the degree of the 0^(th) column of the i^(th) column group(i=0, 1, . . . , K_(ldpc)/M−1) is D_(i) (herein, the degree is thenumber of value 1 existing in each column and all columns belonging tothe same column group have the same degree), and a position (or anindex) of each row where 1 exists in the 0^(th) column of the i^(th)column group is R_(i,0) ⁽⁰⁾, R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i)⁻¹⁾, an index R_(i,j) ^((k)) of a row where k^(th) 1 is located in thej^(th) column in the i^(th) column group is determined by followingEquation 1:R _(i,j) ^((k)) =R _(i,(j−1)) ^((k)) +Q _(ldpc) mod(N _(ldpc) −K_(ldpc))  (1),where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1,2, . . . , M−1.

Equation 1 can be expressed as following Equation 2:R _(i,j) ^((k)) ={R _(i,0) ^((k))+(j mod M)×Q _(ldpc)}mod(N _(ldpc) −K_(ldpc))  (2),where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1,2, . . . , M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 maybe regarded as j.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th)1 is located in the j^(th) column in the i^(th) column group, N_(ldpc)is a length of an LDPC codeword, K_(ldpc) is a length of informationword bits, D_(i) is a degree of columns belonging to the i^(th) columngroup, M is the number of columns belonging to a single column group,and Q_(ldpc) is a size by which each column in the column group iscyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) isknown, the index R_(i,j) ^((k)) of the row where the k^(th) 1 is locatedin the j^(th) column in the i^(th) column group can be known. Therefore,when the index value of the row where the k^(th) 1 is located in the0^(th) column of each column group is stored, a position of column androw where 1 is located in the parity check matrix 200 having theconfiguration of FIG. 20 (that is, in the information word submatrix 210of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging tothe i^(th) column group have the same degree D_(i). Accordingly, theLDPC codeword which stores information on the parity check matrixaccording to the above-described rules may be briefly expressed asfollows.

For example, when N_(ldpc) is 30, K_(ldpc) is 15, and Q_(ldpc) is 3,position information of the row where 1 is located in the 0^(th) columnof the three column groups may be expressed by a sequence of Equations 3and may be referred to as “weight-1 position sequence”.R _(1,0) ⁽¹⁾=1,R _(1,0) ⁽²⁾=2, R _(1,0) ⁽³⁾=8, R _(1,0) ⁽⁴⁾=10,R _(2,0) ⁽¹⁾=0, R _(2,0) ⁽²⁾=9, R _(2,0) ⁽³⁾=13,R _(3,0) ⁽¹⁾=0, R _(3,0) ⁽²⁾=14.  (3),where R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located inthe j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an indexof a row where 1 is located in the 0^(th) column of each column groupmay be briefly expressed as in Table 3 presented below:

TABLE 3   1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having value 1 in the parity checkmatrix, and the i^(th) weight-1 position sequence is expressed byindexes of rows where 1 is located in the 0^(th) column belonging to thei^(th) column group.

The information word submatrix 210 of the parity check matrix accordingto an exemplary embodiment may be defined as in Tables 4 to 12 presentedbelow, based on the above descriptions.

Specifically, Tables 4 to 12 show indexes of rows where 1 is located inthe 0th column of the i^(th) column group of the information wordsubmatrix 210. That is, the information word submatrix 210 is formed ofa plurality of column groups each including M number of columns, andpositions of 1 in the 0^(th) column of each of the plurality of columngroups may be defined by Tables 4 to 12.

Herein, the indexes of the rows where 1 is located in the 0 column ofthe i^(th) column group mean “addresses of parity bit accumulators” The“addresses of parity bit accumulators” have the same meaning as definedin the DVB-C2/S2/T2 standards or the ATSC 3.0 standards which arecurrently being established, and thus, a detailed explanation thereof isomitted.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, thecode rate is 5/15, and M is 360, the indexes of the rows where 1 islocated in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 Indexes of row where 1 is located in the 0th column of the ith icolumn group 0 245 449 491 986 1064 1194 1277 1671 2026 3186 4399 4900528 5413 5558 6570 7492 7768 7837 7984 8306 8483 8685 9357 9642 1004510179 10261 10338 10417 1 1318 1584 1682 1860 1954 2000 2062 3387 34413879 3931 4240 4302 4446 4603 5117 5588 55755793 5955 6097 6221 64496616 7216 7394 9535 9896 10009 10763 2 105 473 785 911 1168 1450 25502851 3277 3624 4128 4460 4572 4669 4783 5102 5133 5199 5905 6647 70287086 7703 8121 8217 9149 9304 9476 9736 9884 3 1217 5338 5737 8334 4 855994 2979 9443 5 7506 7811 9212 9982 6 848 3313 3380 3990 7 2095 41134620 9946 8 1488 2396 5130 7483 9 1002 22417067 10418 10 2008 3199 72157502 11 1161 7705 8194 8534 12 2326 4803 8649 9359 13 125 1880 3177 141141 8033 3072

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 5 or 6presented below:

TABLE 5 Indexes of row where 1 is located in the 0th column of the ith icolumn group 0 553 742 901 1327 1644 2179 2519 3131 3280 3603 3789 37924253 5340 5934 5962 6004 6698 7793 8001 8058 8126 8276 8559 1 503 590598 1185 1266 1336 1806 2473 3021 3356 3490 3680 3936 4501 4659 58916132 6340 6602 7447 8007 8045 8059 8249 2 795 891 947 1330 1502 20412328 2513 2814 2829 4048 4802 6044 6103 6461 6777 6800 7098 7126 80958428 8518 8556 8610 3 601 787 899 1757 2259 2518 2783 2816 2823 29493396 4330 4494 4684 4700 4837 4881 4975 5130 5464 6554 6912 7094 8292 44229 5628 7917 7992 5 1506 3974 4174 5547 6 4278 5650 8208 8533 7 15041747 3433 6345 8 8659 6955 7575 7852 9 607 3002 4913 6453 10 3533 68607895 8048 11 4094 6366 8314 12 2206 4513 5411 13 32 3882 5149 14 6893121 4625 15 1308 4419 6520 16 2092 2373 6849 17 1815 3679 7152 18 35823379 6948 19 1049 2135 3754 20 2276 4442 6591

TABLE 6 Indexes of row where 1 is located in the 0th column of the i ithcolumn group 0 432 655 893 942 1285 1427 1738 2199 2441 2565 2932 32014144 4419 4676 4963 5423 5922 6433 6564 6656 7478 7514 7892 1 220 453690 826 1116 1425 1488 1901 3113 3182 3566 3800 3953 4071 4782 5038 55556836 6871 7131 7609 7850 8317 8443 2 300 454 497 930 1757 2145 2314 23722467 2819 3191 3256 3699 3984 4538 4965 5461 5742 5912 6135 6649 76368078 3455 3 24 65 565 609 990 1319 1394 1465 1918 1975 2463 2987 33303622 4195 4240 4947 5372 6453 6950 7066 8412 8500 8599 4 1373 4668 53242222 5 189 3930 5766 6377 6 3 2961 4207 5747 7 1108 4768 6743 7105 81282 2274 2750 6204 9 2279 2587 2737 6344 10 2883 3164 7275 8040 11 1332734 5081 8386 12 437 3203 7121 13 4280 7128 8490 14 619 4563 6206 152799 6814 6991 16 244 4212 5925 17 1719 7657 8554 18 53 1395 6685 19 5845420 6896 20 2958 5834 8103

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 7 or 8below

TABLE 7 Indexes of row where 1 is located in the 0th column of the ith icolumn group 0 212 255 540 967 1033 1517 1538 3124 3408 3800 4373 48644905 5163 5177 6186 1 275 660 1351 2211 2876 3063 3433 4088 4273 45444618 4632 5548 6101 6111 6136 2 279 335 494 865 1662 1681 3414 3775 4252595 5272 5471 5796 5907 5986 6008 3 345 352 3094 3188 4297 4338 44904865 5303 6477 4 222 681 118 3169 3850 4878 4964 5666 6001 6237 5 172512 1536 1559 2179 2227 3334 4049 6464 6 716 934 1694 2890 3276 36084332 4458 5945 7 1133 1593 1825 2571 3017 4251 5221 5639 5845 8 10761222 6465 9 159 5064 6078 10 174 4073 5357 11 2833 5526 5845 12 15943639 5419 13 1028 1392 4539 14 115 622 2175 15 300 1748 6245 16 27243276 5349 17 1433 6117 6448 18 485 663 4955 19 712 1132 4315 20 177 32664339 21 1171 4841 4982 22 33 1584 3692 23 2820 3485 4249 24 1716 24283125 25 250 2275 6338 26 108 1719 4961

TABLE 8 Indexes of row where 1 is located in the 0th column of the ith icolumn group 0 350 462 1291 1383 1821 2235 2493 3328 3353 3772 3872 39234259 4426 4542 4972 5347 6217 6246 6332 6386 1 177 869 1214 1251 13981482 1737 2014 2161 2331 3108 3297 3438 4388 4430 4456 4522 4783 52736037 6395 2 347 501 658 966 1622 1659 1934 2117 2527 3168 3231 3379 34223739 4218 4497 4894 5000 5167 5728 5975 3 319 398 599 1143 1796 31983521 3886 4139 4453 4556 4636 4688 4753 4986 5199 5224 5496 5698 57246123 4 162 257 304 524 945 1695 1855 2527 2780 2902 2958 3439 348 42244769 4928 5156 5303 5971 6358 6477 5 807 1695 2941 4276 6 2652 2857 46606358 7 329 2100 2412 3632 8 1151 1231 3872 4869 9 1861 3565 5138 5303 10407 794 1455 11 3438 5683 5749 12 1504 1985 3563 13 440 5021 6321 14 1943645 5923 15 1217 1462 5422 16 1212 4715 5973 17 4098 5100 5642 18 55125857 6226 19 2283 5506 5933 20 784 1801 4890 21 4734 4779 4875 22 9385081 5377 23 177 4125 4704 24 1244 2178 3352 25 3689 6350 6465 26 16863465 4336

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 9 or 10below.

TABLE 9 Indexes of row where 1 is located in the 0th column of the ith icolumn group 0 49 719 784 794 968 2382 2685 2873 2974 2995 3540 4179 1272 281 374 1279 2034 2067 2112 3429 3613 3815 3838 4216 2 206 714 8201800 1925 2147 2168 2769 2806 3253 3415 4311 3 62 159 166 605 1496 17112652 3016 3347 3517 3654 4113 4 363 733 1118 2062 2613 2736 3143 34273664 4100 4157 4314 5 57 142 436 983 1364 2105 2113 3074 3639 3835 41644242 6 870 921 950 1212 1361 2128 2707 2993 3730 3968 3983 4227 7 1852684 3263 8 2035 2123 2913 9 883 2221 3821 10 1344 1773 4132 11 438 31733650 12 543 756 1639 13 1057 2337 2898 14 171 3298 3929 15 1626 29603503 16 484 3050 3320 17 2283 2336 4189 18 2732 4132 4318 19 225 23353497 20 600 2246 2658 21 1240 2790 3020 22 301 1097 3539 23 1222 12672594 24 1364 2004 3603 25 1142 1185 2147 26 564 1505 2086 27 697 9912908 28 1467 2073 3462 29 2574 2818 3637 30 748 2527 2772 31 1151 14194129 32 164 1238 3401

TABLE 10 Indexes of row where 1 is located in the 0th column of the ithi column group 0 108 297 703 742 1345 1443 1495 1628 1812 2341 2559 26682810 2877 3442 3690 3755 3904 4264 1 180 211 477 788 824 1090 1272 15781685 1948 2050 2195 2233 2546 2757 2946 3147 3299 3544 2 627 741 11351157 1226 1333 1376 1422 1454 1696 1752 1772 2099 2208 2592 3354 35804066 4242 3 9 795 959 389 1006 1032 1135 1209 1382 1484 1703 1855 19852043 2629 2845 5136 3450 3742 4 230 413 801 829 1108 1170 1291 1759 17931827 1976 2000 2423 2466 2917 3010 3600 3782 4143 5 56 142 236 381 10501141 1372 1627 1985 2247 2340 3023 3434 3519 3957 4013 4142 4164 4279 6298 1211 2548 3643 7 73 1070 1614 1748 8 1439 2141 3614 9 284 1564 262910 607 660 855 11 1195 2037 2753 12 49 1198 2562 13 296 1145 3540 141516 2315 2382 15 154 722 4016 16 759 2375 3825 17 162 194 1749 18 23352422 2632 19 6 1172 2583 20 726 1325 1428 21 985 2208 2269 22 255 28013181 23 2979 3720 4090 24 208 1428 4094 25 199 3743 3757 26 1229 20594282 27 458 1100 1387 28 1199 2481 3284 29 1161 1467 4060 30 959 30144144 31 2666 3960 4123 32 2809 3834 4318

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 11 or 12below.

TABLE 11 Indexes of row where 1 is located in the 0th column of the ithi column group 0 71 334 649 779 786 1124 1131 1267 1379 1554 1766 17981939 1 6 183 364 506 512 922 972 981 1039 1121 1537 1840 2111 2 6 71 153204 253 268 781 799 873 1118 1194 1661 2036 3 6 247 353 581 921 940 11081146 1208 1268 1511 1527 1671 4 6 37 466 548 747 1142 1203 1271 15121516 1837 1904 2125 5 6 171 863 953 1025 1244 1378 1396 1723 1783 18161914 2121 6 1268 1360 1647 1769 7 6 458 1231 1414 8 183 535 1244 1277 9107 360 498 1456 10 6 2007 2059 2120 11 1480 1523 1670 1927 12 139 573711 1790 13 6 1541 1889 2023 14 6 374 957 1174 15 287 423 872 1285 16 61809 1918 17 65 818 1396 18 590 766 2107 19 192 814 1843 20 225 11631256 21 42 735 1415 22 334 1008 2055 23 109 596 1785 24 406 534 1852 25684 719 1543 26 401 465 1040 27 112 392 621 28 82 893 1950 29 887 19622125 30 793 1088 2159 31 723 919 1139 32 610 839 1302 33 218 1030 181634 627 1846 1749 35 496 1165 1742 36 916 1055 1662 37 182 722 945 38 5595 1674

TABLE 12 Indexes of row where 1 is located in the 0th column of the ithi column group 0 32 144 161 199 220 495 510 589 731 806 834 965 12491264 1311 1377 1460 1520 1598 1707 1958 2055 2099 2154 1 20 27 165 462548 583 742 796 1095 1110 1129 1145 1169 1190 1254 1363 1383 1463 17181835 1870 1879 2108 2128 2 288 362 453 505 638 691 745 861 1006 10831124 1175 1247 1275 1337 1353 1378 1506 1588 1632 1720 1868 1980 2135 3405 464 478 511 566 574 641 766 785 802 836 996 1128 1239 1247 1449 14911537 1615 1643 1668 1950 1975 2149 4 86 192 245 357 363 374 700 713 852903 992 1174 1245 1277 1342 1369 1381 1417 1463 1712 1800 1962 2053 21185 101 327 378 550 6 186 723 1318 1550 7 118 277 504 1835 8 199 407 17761965 9 387 1253 1328 1975 10 62 144 1163 2017 11 100 475 572 2136 12 431865 1568 2055 13 283 640 981 1172 14 2201038 1903 2147 15 483 1318 13582118 16 92 961 1709 1810 17 112 403 1485 2042 18 431 1130 1365 19 5871005 1206 1588 20 704 1113 1943 21 175 1487 2100 22 1507 1950 2110 23962 1613 20358 24 554 1295 1501 25 488 784 1446 26 871 1935 1964 27 541475 1504 28 1579 1617 2074 29 1856 1967 2131 30 330 1582 2107 31 401056 1809 32 1310 1353 1410 33 232 554 1939 34 168 641 1099 35 333 4371556 36 153 622 745 37 719 931 1188 38 2347 638 1607

In the above-described examples, the length of the LDPC codeword is16200 and the code rate is 5/15, 7/15, 9/15, 11/15, and 13/15. However,this is merely an example and the position of 1 in the information wordsubmatrix 210 may be defined variously when the length of the LDPCcodeword is 64800 or the code rate has different values.

Meanwhile, even when the order of numbers in a sequence corresponding tothe i^(th) column group of the parity check matrix 200 as shown in theabove-described Tables 4 to 12 is changed, the changed parity checkmatrix is a parity check matrix used for the same code. Therefore, acase in which the order of numbers in the sequence corresponding to thei^(th) column group in Tables 4 to 12 is changed is covered by theinventive concept.

According to an exemplary embodiment, even when the arrangement order ofsequences corresponding to each column group is changed in Tables 4 to12, cycle characteristics on a graph of a code and algebraiccharacteristics such as degree distribution are not changed. Therefore,a case in which the arrangement order of the sequences shown in Tables 4to 12 is changed is also covered by the inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to allsequences corresponding to a certain column group in Tables 4 to 12, thecycle characteristics on the graph of the code or the algebraiccharacteristics such as degree distribution are not changed. Therefore,a result of equally adding a multiple of Q_(ldpc) to the sequences shownin Tables 4 to 12 is also covered by the inventive concept. However, itshould be noted that, when the resulting value obtained by adding themultiple of Q_(ldpc) to a given sequence is greater than or equal to(N_(ldpc)−K_(ldpc)), a value obtained by applying a modulo operation for(N_(ldpc)−K_(ldpc)) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^(th) column of thei^(th) column group of the information word submatrix 210 are defined asshown in Tables 4 to 12, positions of rows where 1 exists in anothercolumn of each column group may be defined since the positions of therows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc)in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th)column group of the information word submatrix 210, 1 exists in the553^(th) row, 742^(nd) row, 901^(st) row, . . . .

In this case, since Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M=(16200−5400)/360=30,the indexes of the rows where 1 is located in the 1^(st) column of the0^(th) column group may be 584=553+30), 931(=901+30), . . . , and theindexes of the rows where 1 is located in the 2^(nd) column of the0^(th) column group may be 607(=577+30), 796(=766+30), 955(=925+30), . .. .

In the above-described method, the indexes of the rows where 1 islocated in all rows of each column group may be defined.

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 20may be defined as follows:

The parity submatrix 220 includes N_(ldpc)−K_(ldpc) number of columns(that is, K_(ldpc) ^(th) column to (N_(ldpc)−1)^(th) column), and has adual diagonal or staircase configuration. Accordingly, the degree ofcolumns except the last column (that is, (N_(ldpc)−1)^(th) column) fromamong the columns included in the parity submatrix 220 is 2, and thedegree of the last column is 1.

As a result, the information word submatrix 210 of the parity checkmatrix 200 may be defined by Tables 4 to 12, and the parity submatrix220 of the parity check matrix 200 may have a dual diagonalconfiguration.

When the columns and rows of the parity check matrix 200 shown in FIG.20 are permutated based on Equation 4 and Equation 5, the parity checkmatrix shown in FIG. 20 may be changed to a parity check matrix 300shown in FIG. 21 .Q _(ldpc) ·i+j⇒M·j+i (0≤i<M, 0≤j<Q _(ldpc))  (4)K _(ldpc) +Q _(ldpc) ·k+l⇒K _(ldpc) +M·l+k (0≤k<M, 0≤l<Q _(ldpc))  (5)

The method for permutating based on Equation 4 and Equation 5 will beexplained below. Since row permutation and column permutation apply thesame principle, the row permutation will be explained by the way of anexample.

In the case of the row permutation, regarding the X^(th) row, i and jsatisfying X=Q_(ldpc)×i+j are calculated and the X^(th) row ispermutated by assigning the calculated i and j to M×j+i. For example,regarding the 7^(th) row, i and j satisfying 7=2×i+j are 3 and 1,respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row(10×1+3=13).

When the row permutation and the column permutation are performed in theabove-described method, the parity check matrix of FIG. 20 may beconverted into the parity check matrix of FIG. 21 .

Referring to FIG. 21 , the parity check matrix 300 is divided into aplurality of partial blocks, and a quasi-cyclic matrix of M×Mcorresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration ofFIG. 21 is formed of matrix units of M×M. That is, the submatrices ofM×M are arranged in the plurality of partial blocks, constituting theparity check matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matricesof M×M, M number of columns may be referred to as a column block and Mnumber of rows may be referred to as a row block. Accordingly, theparity check matrix 300 having the configuration of FIG. 21 is formed ofN_(qc_column)=N_(ldpc)/M number of column blocks andN_(qc_row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc_column)−1)^(th) column block A(330) of the 0^(th) rowblock has a form shown in Equation 6 presented below:

$\begin{matrix}{A = \begin{bmatrix}0 & 0 & \ldots & 0 & 0 \\1 & 0 & \ldots & 0 & 0 \\0 & 1 & \ldots & 0 & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots \\0 & 0 & \ldots & 1 & 0\end{bmatrix}} & (6)\end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row andthe (M−1)^(th) column are all “0”, and, regarding 0≤i≤(M−2), the(i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−1 in the parity submatrix320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block isconfigured by a unit matrix I_(M×M) 340. In addition, regarding0≤i≤(N_(ldpc)−K_(ldpc))/M−2, the (i+1)^(th) row block of the(K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M)340.

Third, a block 350 constituting the information word submatrix 310 mayhave a cyclic-shifted format of a cyclic matrix P, P^(a) ^(g) , or anadded format of the cyclic-shifted matrix p^(a) ^(g) of the cyclicmatrix P (or an overlapping format).

For example, a format of the block P 350 in which the upper suffix aijof P is 1 (that is, P¹) of cyclic matrix P may be expressed by Equation7 presented below:

$\begin{matrix}{P = \begin{bmatrix}0 & 1 & 0 & & 0 \\0 & 0 & 1 & \ldots & 0 \\ \vdots & \vdots & \vdots & & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & & 0\end{bmatrix}} & (7)\end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is amatrix in which a weight of each of M number of rows is 1 and a weightof each of M number of columns is 1. When a_(ij) is 0, the cyclic matrixP, that is, P⁰ indicates a unit matrix I_(M×M). And, for convenience ofindication, when a_(ij) is ∞, P^(∞) is defined as a zero matrix.

A submatrix existing where the i^(th) row block and the j^(th) columnblock intersect in the parity check matrix 300 of FIG. 21 may be P^(a)^(g) . Accordingly, i and j indicate the number of row blocks and thenumber of column blocks in the partial blocks corresponding to theinformation word. Accordingly, in the parity check matrix 300, the totalnumber of columns is N_(ldpc)=M×N_(qc_column), and the total number ofrows is N_(parity)=M×N_(qc_row). That is, the parity check matrix 300 isformed of N_(qc_column) number of “column blocks” and N_(qc_row) numberof “row blocks”.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 200 as shown in FIG. 20 will be explained. An LDPC encodingprocess when the parity check matrix 200 is defined as shown in Table 4by way of an example will be explained for the convenience ofexplanation.

First, when information word bits having a length of K_(ldpc) are [i₀,i₁, i₂, . . . , i_(K) _(ldpc) ⁻¹], and parity bits having a length ofN_(ldpc)−K_(ldpc) are [p₀, p₁, p₂, . . . p_(N) _(ldpc) _(−K) _(lpdc)⁻¹], the LDPC encoding is performed by the following process.

Step 1) Parity bits are initialized as ‘0’. That is, p₀=p₁==p₂= . . .=p_(N) _(ldpc) _(−K) _(lpdc) ⁻¹=0.

Step 2) The 0^(th) information word bit i₀ is accumulated in a paritybit having the address of the parity bit defined in the first row (thatis, the row of i=0) of table 4 as the index of the parity bit. This maybe expressed by Equation 8 presented below:P ₂₄₅ =P ₂₄₅ ⊕i ₀ P ₆₅₇₀ =P ₆₅₇₀ ⊕i ₀P ₄₄₉ =P ₄₄₉ ⊕i ₀ P ₇₄₉₂ =P ₇₄₉₂ ⊕i ₀P ₄₉₁ =P ₄₉₁ ⊕i ₀ P ₇₇₆₈ =P ₇₇₆₈ ⊕i ₀P ₉₈₀ =P ₉₈₀ ⊕i ₀ P ₇₈₃₇ =P ₇₈₃₇ ⊕i ₀P ₁₀₆₄ =P ₁₀₆₄ ⊕i ₀ P ₇₉₈₄ =P ₇₉₈₄ ⊕i ₀P ₁₁₉₄ =P ₁₁₉₄ ⊕i ₀ P ₈₃₀₆ =P ₈₃₀₆ ⊕i ₀P ₁₂₇₇ =P ₁₂₇₇ ⊕i ₀ P ₈₄₈₃ =P ₈₄₈₃ ⊕i ₀P ₁₆₇₁ =P ₁₆₇₁ ⊕i ₀ P ₈₆₈₅ =P ₈₆₈₅ ⊕i ₀P ₂₀₂₆ =P ₂₀₂₅ ⊕i ₀ P ₉₃₅₇ =P ₉₃₅₇ ⊕i ₀P ₃₁₈₆ =P ₃₁₈₅ ⊕i ₀ P ₉₆₄₂ =P ₉₆₄₂ ⊕i ₀P ₄₃₉₉ =P ₄₃₉₉ ⊕i ₀ P ₁₀₀₄₅ =P ₁₀₀₄₅ ⊕i ₀P ₄₉₀₀ =P ₄₉₀₀ ⊕i ₀ P ₁₀₁₇₉ =P ₁₀₁₇₉ ⊕i ₀P ₅₂₈₃ =P ₅₂₈₃ ⊕i ₀ P ₁₀₂₆₁ =P ₁₀₂₆₁ ⊕i ₀P ₅₄₁₃ =P ₅₄₁₃ ⊕i ₀ P ₁₀₃₃₈ =P ₁₀₃₃₈ ⊕i ₀P ₅₅₅₈ =P ₅₅₅₈ ⊕i ₀ P ₁₀₄₁₂ =P ₁₀₄₁₂ ⊕i ₀  (8)

Herein, i₀ is a 0^(th) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 3) The other 359 information word bits i_(m) (m=1, 2, . . . , 359)are accumulated in the parity bit. The other information word bits maybelong to the same column group as that of i₀. In this case, the addressof the parity bit may be determined based on Equation 9 presented below:(x+(m mod 360)×Q _(ldpc))mod(N _(ldpc) −K _(ldpc))  (9)

Herein, x is an address of a parity bit accumulator corresponding to theinformation word bit i₀, and Q_(ldpc) is a size by which each column iscyclic-shifted in the information word submatrix, and may be 108 in thecase of table 4. In addition, since m=1, 2, . . . , 359, (m mod 360) inEquation 9 may be regarded as m.

As a result, information word bits i_(m) (m=1, 2, . . . , 359) areaccumulated in the parity bits having the address of the parity bitcalculated based on Equation 9 as the index. For example, an operationas shown in Equation 10 presented below may be performed for theinformation word bit i₁:P ₂₇₅ =P ₂₇₅ ⊕i ₁ P ₆₆₀₀ =P ₆₆₀₀ ⊕i ₁P ₄₇₉ =P ₄₇₉ ⊕i ₁ P ₇₅₂₂ =P ₇₅₂₂ ⊕i ₁P ₅₂₁ =P ₅₂₁ ⊕i ₁ P ₇₇₉₈ =P ₇₇₉₈ ⊕i ₁P ₁₀₁₀ =P ₁₀₁₀ ⊕i ₁ P ₇₈₆₇ =P ₇₈₆₇ ⊕i ₁P ₁₀₉₄ =P ₁₀₉₄ ⊕i ₁ P ₈₀₁₄ =P ₈₀₁₄ ⊕i ₁P ₁₂₂₄ =P ₁₂₂₄ ⊕i ₁ P ₈₃₃₆ =P ₈₃₃₆ ⊕i ₁P ₁₃₀₇ =P ₁₃₀₇ ⊕i ₁ P ₈₅₁₃ =P ₈₅₁₃ ⊕i ₁P ₁₇₀₁ =P ₁₇₀₁ ⊕i ₁ P ₈₇₁₅ =P ₈₇₁₅ ⊕i ₁P ₂₀₅₆ =P ₂₀₅₅ ⊕i ₁ P ₉₃₈₇ =P ₉₃₈₇ ⊕i ₁P ₃₂₁₆ =P ₃₂₁₅ ⊕i ₁ P ₉₆₇₂ =P ₉₆₇₂ ⊕i ₁P ₄₄₂₉ =P ₄₄₂₉ ⊕i ₁ P ₁₀₀₇₅ =P ₁₀₀₇₅ ⊕i ₁P ₄₉₃₀ =P ₄₉₃₀ ⊕i ₁ P ₁₀₂₀₉ =P ₁₀₂₀₉ ⊕i ₁P ₅₃₁₃ =P ₅₃₁₃ ⊕i ₁ P ₁₀₂₉₁ =P ₁₀₂₉₁ ⊕i ₁P ₅₄₄₃ =P ₅₄₄₃ ⊕i ₁ P ₁₀₃₆₈ =P ₁₀₃₆₈ ⊕i ₁P ₅₅₈₈ =P ₅₅₈₈ ⊕i ₁ P ₁₀₄₄₂ =P ₁₀₄₄₂ ⊕i ₁  (10)

Herein, i₁ is a 1^(st) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 4) The 360^(th) information word bits i₃₆₀ is accumulated in aparity bit having the address of the parity bit defined in the 2^(nd)row (that is, the row of i=1) of table 4 as the index of the parity bit.

Step 5) The other 359 information word bits belonging to the same groupas that of the information word bit i₃₆₀ are accumulated in the paritybit. In this case, the address of the parity bit may be determined basedon Equation 9. However, in this case, x is the address of the parity bitaccumulator corresponding to the information word bit i₃₆₀.

Step 6) Steps 4 and 5 described above are repeated for all of the columngroups of table 4.

Step 7) As a result, a parity bit p_(i) is calculated based on Equation11 presented below. In this case, i is initialized as 1.P _(i) =p _(i) ⊕p _(i−1)=1,2, . . . N _(ldpc) −K _(ldpc)−1  (11)

In Equation 11, p_(i) is an ith parity bit, N_(ldpc) is a length of anLDPC codeword, K_(ldpc) is a length of an information word of the LDPCcodeword, and ⊕ is a binary operation.

As a result, the encoder 110 may calculate the parity bits according tothe above-described method.

In another example, a parity check matrix according to an exemplaryembodiment may have a configuration as shown in FIG. 22 .

Referring to FIG. 22 , the parity check matrix 400 may be formed of 5matrices A, B, C, Z, and D. Hereinafter, the configuration of eachmatrix will be explained to explain the configuration of the paritycheck matrix 400.

First, M₁, M₂, Q₁, and Q₂, which are parameter values related to theparity check matrix 400 as shown in FIG. 22 , may be defined as shown intable 13 presented below according to the length and the code rate ofthe LDPC codeword.

TABLE 13 Sizes Rate Length M₁ M₂ Q_(i) Q_(i) 1/15 16200 2520 12600 7 3564800 1080 59400 3 165 2/15 16200 3240 10800 9 30 64800 1800 54360 5 1513/15 16200 1080 11880 3 33 64800 1800 50040 5 139 4/15 16200 1080 108003 30 64800 1800 45720 5 127 5/15 16200 720 10080 2 28 64800 1440 41760 4116 6/15 16200 1080 8640 3 24 64800 1080 37800 3 105

The matrix A is formed of K number of columns and g number of rows, andthe matrix C is formed of K+g number of columns and N−K−g number ofrows. Herein, K is a length of information word bits, and N is a lengthof the LDPC codeword.

Indexes of rows where 1 is located in the 0^(th) column of the ithcolumn group in the matrix A and the matrix C may be defined based ontable 14 according to the length and the code rate of the LDPC codeword.In this case, an interval at which a pattern of a column is repeated ineach of the matrix A and the matrix C, that is, the number of columnsbelonging to the same group, may be 360.

For example, when the length N of the LDPC codeword is 16200 and thecode rate is 5/15, the indexes of rows where 1 is located in the 0^(th)column of the ith column group in the matrix A and the matrix C aredefined as shown in table 14 presented below:

TABLE 14 Indexes of row where 1 is located in the 0th column of i theith column group 0 69 244 706 5145 5994 6066 6763 6815 8509 1 257 541618 3933 6188 7048 7484 8424 9104 2 69 500 536 1494 1664 7075 7553 82023 11 189 340 2103 3199 6775 7471 7918 10530 4 333 400 434 1806 1264 56938534 9274 10344 5 111 129 260 3562 3676 3680 3809 5169 7308 8280 6 100303 342 3133 3952 4226 4713 5053 5717 9931 7 83 87 374 828 2460 49436311 8657 9272 9571 8 114 166 325 2680 4698 7703 7886 8791 9978 10684 9281 542 549 1671 3178 3955 7453 7432 9052 10219 10 202 271 608 3860 41734203 5169 6871 8113 9757 11 16 359 419 3333 4198 4737 6170 7987 957310095 12 235 244 584 4640 5007 5563 6029 6816 7678 9968 13 123 443 6462460 3845 4151 6610 7245 7686 8651 14 136 231 468 835 2622 3292 51585294 6584 9926 15 3085 4683 8194 9027 9922 9928 10550 16 2462 3185 39764091 8089 8772 9342

In the above-described example, the length of the LDPC codeword is 16200and the code rate 5/15. However, this is merely an example and theindexes of rows where 1 is located in the 0^(th) column of the ithcolumn group in the matrix A and the matrix C may be defined variouslywhen the length of the LDPC codeword is 64800 or the code rate hasdifferent values.

Hereinafter, positions of rows where 1 exists in the matrix A and thematrix C will be explained with reference to table 14 by way of anexample.

Since the length N of the LDPC codeword is 16200 and the code rate is5/15 in table 10, M₁=720, M₂=10080, Q₁=2 and Q₂=28 in the parity checkmatrix 400 defined by table 14 with reference to table 12.

Herein, Q₁ is a size by which columns of the same column group arecyclic-shifted in the matrix A, and Q₂ is a size by which columns of thesame column group are cyclic-shifted in the matrix C.

In addition, Q₁=M₁/L, Q₂=M₂/L, M₁=g, and M₂=N−K−g, and L is an intervalat which a pattern of a column is repeated in the matrix A and thematrix C, and for example, may be 360.

The index of the row where 1 is located in the matrix A and the matrix Cmay be determined based on the M₁ value.

For example, since M₁=720 in the case of table 14, the positions of therows where 1 exists in the 0^(th) column of the ith column group in thematrix A may be determined based on values smaller than 720 from amongthe index values of table 14, and the positions of the rows where 1exists in the 0^(th) column of the ith column group in the matrix C maybe determined based on values greater than or equal to 720 from amongthe index values of table 14.

Specifically, in table 14, the sequence corresponding to the 0^(th)column group is “69, 244, 706, 5145, 5994, 6066, 6763, 6815, and 8509”.Accordingly, in the case of the 0^(th) column of the 0^(th) column groupof the matrix A, 1 may be located in the 69^(th) row, 244^(th) row, and706^(th) row, and, in the case of the 0^(th) column of the 0^(th) columngroup of the matrix C, 1 may be located in the 5145^(th) row, 5994^(th)row, 6066^(th) row, 6763^(rd) row, 6815^(th) row, and 8509^(th) row.

Once positions of 1 in the 0^(th) column of each column group of thematrix A are defined, positions of rows where 1 exists in another columnof each column group may be defined by cyclic-shifting from the previouscolumn by Q_(i). Once positions of 1 in the 0^(th) column of each columngroup of the matrix C are defined, position of rows where 1 exists inanother column of each column group may be defined by cyclic-shiftingfrom the previous column by Q₂.

In the above-described example, in the case of the 0^(th) column of the0^(th) column group of the matrix A, 1 exists in the 69^(th) row,244^(th) row, and 706^(th) row. In this case, since Q₁=2, the indexes ofrows where 1 exists in the 1^(st) column of the 0^(th) column group are71(=69+2), 246(=244+2), and 708(=706+2), and the index of rows where 1exists in the 2^(nd) column of the 0^(th) column group are 73(=71+2),248 (=246+2), and 710(=708+2).

In the case of the 0^(th) column of the 0^(th) column group of thematrix C, 1 exists in the 5145^(th) row, 5994^(th) row, 6066^(th) row,6763^(rd) row, 6815^(th) row, and 8509^(th) row. In this case, sinceQ₂=28, the index of rows where 1 exists in the 1^(st) column of the0^(th) column group are 5173(=5145+28), 6022(=5994+28), 6094 (6066+28),6791(=6763+28), 6843(=6815+28), and 8537(=8509+28) and the indexes ofrows where 1 exists in the 2^(nd) column of the 0^(th) column group are5201(=5173+28), 6050(=6022+28), 6122(=6094+28), 6819(=6791+28),6871(=6843+28), and 8565(=8537+28).

In this method, the positions of rows where 1 exists in all columngroups of the matrix A and the matrix C are defined.

The matrix B may have a dual diagonal configuration, the matrix D mayhave a diagonal configuration (that is, the matrix D is an identitymatrix), and the matrix Z may be a zero matrix.

As a result, the parity check matrix 400 shown in FIG. 22 may be definedby the matrices A, B, C, D, and Z having the above-describedconfigurations.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 400 shown in FIG. 22 will be explained. An LDPC encodingprocess when the parity check matrix 400 is defined as shown in Table 14by way of an example will be explained for the convenience ofexplanation.

For example, when an information word block S=(s₀, s₁, . . . , S_(K−1))is LDPC-encoded, an LDPC codeword Λ=(λ₀, λ₁, . . . , λ_(N−1))=(s₀, s₁, .. . , S_(K−1), p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ⁻¹) including a paritybit P=(p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ⁻¹) may be generated.

M₁ and M₂ indicate the size of the matrix B having the dual diagonalconfiguration and the size of the matrix C having the diagonalconfiguration, respectively, and M₁=g, M₂=N−K−g.

A process of calculating a parity bit is as follows. In the followingexplanation, the parity check matrix 400 is defined as shown in table 14by way of an example, for the convenience of explanation.

Step 1) λ and p are initialized as λ_(i)=s_(i) (i=0, 1, . . . , K−1),p_(j)=0 (j=0, 1, . . . , M₁+M₂−1).

Step 2) The 0^(th) information word bit λ₀ is accumulated in the addressof the parity bit defined in the first row (that is, the row of i=0) oftable 14. This may be expressed by Equation 12 presented below:P ₆₉ =P ₆₉⊕λ₀ P ₆₀₆₆ =P ₆₀₆₆⊕λ₀P ₂₄₄ =P ₂₄₄⊕λ₀ P ₆₇₆₃ =P ₆₇₆₃⊕λ₀P ₇₀₆ =P ₇₀₆⊕λ₀ P ₆₈₁₅ =P ₆₈₁₅⊕λ₀P ₅₁₅₄ =P ₅₁₅₄⊕λ₀ P ₈₅₀₉ =P ₈₅₀₉⊕λ₀P ₅₉₉₄ =P ₅₉₉₄⊕λ₀  (12)

Step 3) Regarding the next L−1 number of information word bits λ_(m)(m=1, 2, . . . , L−1), λ_(m) is accumulated in the parity bit addresscalculated based on Equation 13 presented below:(χ+m×Q ₁)mod M ₁ (if χ<M ₁)M ₁+{(χ−M ₁ +m×Q ₂)mod M ₂} (if χ≥M ₁)  (13)

Herein, x is an address of a parity bit accumulator corresponding to the0^(th) information word bit λ₀.

In addition. Q₁=M₁/L and Q₂=M₂/L In addition, since the length N of theLDPC codeword is 16200 and the code rate is 5/15 in table 14, M₁=1080,M₂=37800, Q₁=3, Q₂=105, and L=360 with reference to table 13.

Accordingly, an operation as shown in Equation 14 presented below may beperformed for the 1^(st) information word bit λ₁:P ₇₁ =P ₇₁⊕λ₁ P ₆₀₉₄ =P ₆₀₉₄⊕λ₁P ₂₄₆ =P ₂₄₆⊕λ₁ P ₆₇₉₁ =P ₆₇₉₁⊕λ₁P ₇₀₈ =P ₇₀₈⊕λ₁ P ₆₈₄₃ =P ₆₈₄₃⊕λ₁P ₅₁₇₃ =P ₅₁₇₃⊕λ₁ P ₈₅₃₇ =P ₈₅₃₇⊕λ₁P ₆₀₂₂ =P ₆₀₂₂⊕λ₁  (14)

Step 4) Since the same address of the parity bit as in the second row(that is the row of i=1) of table 14 is given to the Lth informationword bit λ_(L), in a similar method to the above-described method, theaddress of the parity bit regarding the next L−1 number of informationword bits λ_(m) (m=L+1, L+2, 2L−1) is calculated based on Equation 13.In this case, x is the address of the parity bit accumulatorcorresponding to the information word bit λ_(L), and may be obtainedbased on the second row of table 14.

Step 5) The above-described processes are repeated for L number of newinformation word bits of each group by considering new rows of table 14as the address of the parity bit accumulator.

Step 6) After the above-described processes are repeated for thecodeword bits λ₀ to λ_(K−1), values regarding Equation 15 presentedbelow are calculated in sequence from i=1:P _(i) =P _(i) ⊕P _(i−1) (i=1,2, . . . ,M ₁−1)  (15)

Step 7) Parity bits λ_(K) to λ_(K+M) ₁ ⁻¹ corresponding to the matrix Bhaving the dual diagonal configuration are calculated based on Equation16 presented below:λ_(K+L×t+s) =p _(Q) ₁ _(×S+t) (0≤s<L, 0≤t<Q ₁)  (16)

Step 8) The address of the parity bit accumulator regarding L number ofnew codeword bits λ_(K) to λ_(K+M) ₁ ⁻¹ of each group is calculatedbased on table 14 and Equation 13.

Step 9) After the codeword bits λ_(K) to λ_(K+M) ₁ ⁻¹ are calculated,parity bits λ_(K+M) ₁ to λ_(K+M) ₁ _(M) ₂ ⁻¹ corresponding to the matrixC having the diagonal configuration are calculated based on Equation 17presented below:λ_(K+M) ₁ _(+L×t+s) =p _(M) ₁ _(+Q) ₂ _(×S+t) (0≤s<L, 0≤t<Q ₂)  (17)

As a result, the parity bits may be calculated in the above-describedmethod.

Referring back to FIG. 19 , the encoder 110 may perform the LDPCencoding by using various code rates such as 3/15, 4/15, 5/15, 6/15,7/15, 8/15, 9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, theencoder 110 may generate an LDPC codeword having various lengths such as16200, 64800, etc., based on the length of the information word bits andthe code rate.

In this case, the encoder 110 may perform the LDPC encoding by using theparity check matrix, and the parity check matrix is configured as shownin FIGS. 20 to 22 .

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem(BCH) encoding as well as LDPC encoding. To achieve this, the encoder110 may further include a BCH encoder (not shown) to perform BCHencoding.

In this case, the encoder 110 may perform encoding in an order of BCHencoding and LDPC encoding. Specifically, the encoder 110 may add BCHparity bits to input bits by performing BCH encoding and LDPC-encodesthe information word bits including the input bits and the BCH paritybits, thereby generating the LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, theinterleaver 120 receives the LDPC codeword from the encoder 110, andinterleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword suchthat a bit included in a predetermined bit group from among a pluralityof bit groups constituting the LDPC codeword (that is, a plurality ofgroups or a plurality of blocks) is mapped onto a predetermined bit of amodulation symbol. Accordingly, the modulator 130 may map a bit includedin a predetermined group from among the plurality of groups of the LDPCcodeword onto a predetermined bit of the modulation symbol.

To achieve this, as shown in FIG. 23 , the interleaver 120 may include aparity interleaver 121, a group interleaver (or a group-wise interleaver122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves the parity bits constituting theLDPC codeword.

Specifically, when the LDPC codeword is generated based on the paritycheck matrix 200 having the configuration of FIG. 20 , the parityinterleaver 121 may interleave only the parity bits of the LDPC codewordby using Equation 18 presented below:u _(i) =c _(i) for 0≤i<K _(ldpc), andu _(K) _(ldpc) _(+M·t+s) =c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) (0≤s<M,0≤t<Q _(ldpc))  (18),where M is an interval at which a pattern of a column group is repeatedin the information word submatrix 210, that is, the number of columnsincluded in a column group (for example, M=360), and Q_(ldpc) is a sizeby which each column is cyclic-shifted in the information word submatrix210. That is, the parity interleaver 121 performs parity interleavingwith respect to the LDPC codeword c=(c₀, c₁, . . . , c_(N) _(ldpc) ⁻¹),and outputs U=(u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹).

The LDPC codeword parity-interleaved in the above-described method maybe configured such that a predetermined number of continuous bits of theLDPC codeword have similar decoding characteristics (cycle distribution,a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on thebasis of M number of continuous bits. Herein, M is an interval at whicha pattern of a column group is repeated in the information wordsubmatrix 210 and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity checkmatrix should be “0”. This means that a sum of products of the i^(th)LDPC codeword bit, c_(i) (i=0, 1, . . . , N_(ldpc)−1) and the i^(th)column of the parity check matrix should be a “0” vector. Accordingly,the i^(th) LDPC codeword bit may be regarded as corresponding to thei^(th) column of the parity check matrix.

In the case of the parity check matrix 200 of FIG. 20 , M number ofcolumns in the information word submatrix 210 belong to the same groupand the information word submatrix 210 has the same characteristics onthe basis of a column group (for example, the columns belonging to thesame column group have the same degree distribution and the same cyclecharacteristic).

In this case, since M number of continuous bits in the information wordbits correspond to the same column group of the information wordsubmatrix 210, the information word bits may be formed of M number ofcontinuous bits having the same codeword characteristics. When theparity bits of the LDPC codeword are interleaved by the parityinterleaver 121, the parity bits of the LDPC codeword may be formed of Mnumber of continuous bits having the same codeword characteristics.

However, regarding the LDPC codeword encoded based on the parity checkmatrix 300 of FIG. 21 and the parity check matrix 400 of FIG. 22 ,parity interleaving may not be performed. In this case, the parityinterleaver 121 may be omitted.

The group interleaver 122 may divide the parity-interleaved LDPCcodeword into a plurality of bit groups and rearrange the order of theplurality of bit groups in bit group wise (or bit group unit). That is,the group interleaver 122 may interleave the plurality of bit groups inbit group wise.

To achieve this, the group interleaver 122 divides theparity-interleaved LDPC codeword into a plurality of bit groups by usingEquation 19 or Equation 20 presented below.

$\begin{matrix}{X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\}{for}O} \leq j < N_{group}}} & (19) \\{X_{j} = {{\left\{ {\left. u_{k} \middle| {{360 \times j} \leq k < {360 \times \left( {j + 1} \right)}} \right.,{0 \leq k < N_{ldpc}}} \right\}{for}0} \leq j < N_{group}}} & (20)\end{matrix}$where N_(group) is the total number of bit groups, X_(j) is the i^(th)bit group, and u_(k) is the k^(th) LDPC codeword bit input to the groupinterleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M atwhich the pattern of a column group is repeated in the information wordsubmatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of bit groups maybe as shown in FIG. 24 .

Referring to FIG. 24 , the LDPC codeword is divided into the pluralityof bit groups and each bit group is formed of M number of continuousbits. When M is 360, each of the plurality of bit groups may be formedof 360 bits. Accordingly, the bit groups may be formed of bitscorresponding to the column groups of the parity check matrix.

Specifically, since the LDPC codeword is divided by M number ofcontinuous bits, K_(ldpc) number of information word bits are dividedinto (K_(ldpc)/M) number of bit groups and N_(ldpc)−K_(ldpc) number ofparity bits are divided into (N_(ldpc)−K_(ldpc))/M number of bit groups.Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) numberof bit groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is16200, the number of groups N_(group)s constituting the LDPC codeword is45(=16200/360), and, when M=360 and the length N_(ldpc) of the LDPCcodeword is 64800, the number of bit groups N_(group) constituting theLDPC codeword is 180(=64800/360).

As described above, the group interleaver 122 divides the LDPC codewordsuch that M number of continuous bits are included in a same group sincethe LDPC codeword has the same codeword characteristics on the basis ofM number of continuous bits. Accordingly, when the LDPC codeword isgrouped by M number of continuous bits, the bits having the samecodeword characteristics belong to the same group.

In the above-described example, the number of bits constituting each bitgroup is M. However, this is merely an example and the number of bitsconstituting each bit group is variable.

For example, the number of bits constituting each bit group may be analiquot part of M. That is, the number of bits constituting each bitgroup may be an aliquot part of the number of columns constituting acolumn group of the information word submatrix of the parity checkmatrix. In this case, each bit group may be formed of aliquot part of Mnumber of bits. For example, when the number of columns constituting acolumn group of the information word submatrix is 360, that is, M=360,the group interleaver 122 may divide the LDPC codeword into a pluralityof bit groups such that the number of bits constituting each bit groupis one of the aliquot parts of 360.

In the following explanation, the number of bits constituting a bitgroup is M by way of an example, for the convenience of explanation.

Thereafter, the group interleaver 122 interleaves the LDPC codeword inbit group wise. Specifically, the group interleaver 122 may group theLDPC codeword into the plurality of bit groups and rearrange theplurality of bit groups in bit group wise. That is, the groupinterleaver 122 changes positions of the plurality of bit groupsconstituting the LDPC codeword and rearranges the order of the pluralityof bit groups constituting the LDPC codeword in bit group wise.

Herein, the group interleaver 122 may rearrange the order of theplurality of bit groups in bit group wise such that bit groups includingbits mapped onto the same modulation symbol from among the plurality ofbit groups are spaced apart from one another at predetermined intervals.

In this case, the group interleaver 122 may rearrange the order of theplurality of bit groups in bit group wise by considering at least one ofthe number of rows and columns of the block interleaver 124, the numberof bit groups of the LDPC codeword, and the number of bits included ineach bit group, such that bit groups including bits mapped onto the samemodulation symbol are spaced apart from one another at predeterminedintervals.

To achieve this, the group interleaver 122 may rearrange the order ofthe plurality of groups in bit group wise by using Equation 21 presentedbelow:Y _(j) =X _(π(j)) (0≤j<N _(group))  (21),where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a modulation method, and a coderate. That is, π(j) denotes a permutation order for group wiseinterleaving.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before groupinterleaving, and Equation 21 means that the pre-interleaving π(j)^(th)bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be definedas in Tables 15 to 27 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bit group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 5/15 to generate an LDPC codeword of a length of 16200, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 16200 and the code rateof 5/15 in tables 15 to 27 presented below.

For example, when the length of the LDPC codeword is 16200, the coderate is 5/15, and the modulation method (or modulation format) is16-Quadrature Amplitude Modulation (QAM), π(j) may be defined as intable 15 presented below. In particular, table 15 may be applied whenLDPC encoding is performed based on the parity check matrix defined bytable 14.

TABLE 15 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block 3 33 39 2 38 29 0 10 25 17 7 2144 37 8 34 20 1 4 31 11 42 22 of Group-wise 13 12 28 26 43 30 14 16 2324 15 5 18 9 36 6 19 32 40 41 35 27 interleaver input

In the case of Table 15, Equation 21 may be expressed as Y₀=X_(π(0))=X₃,Y₁=X_(π(1))=X₃₃, Y₂=X_(π(2))=X₃₉, . . . , Y₄₃=X_(π(43))=X₃₅,Y₄₄=X_(π(44))=X₂₇. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 3^(rd) bit group to the 0^(th) bit group, the 33^(rd) bit group tothe 1^(st) bit group, the 39^(th) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 27^(th) bitgroup to the 44^(th) bit group. Herein, the changing the Ath bit groupto the Bth bit group means rearranging the order of bit groups so thatthe Ath bit group is to be the Bth bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 7/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 16 presented below. In particular, table 16 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 5.

TABLE 16 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block 20 13 11 12 6 3 15 8 18 33 14 170 21 19 39 35 16 42 26 10 9 31 of Group-wise 30 5 7 2 24 29 37 23 4 3432 27 25 41 44 36 28 43 22 40 1 38 interleaver input

In the case of Table 16, Equation 21 may be expressed asY₀=X_(π(0))=X₂₀, Y₁=X_(π(1))=X₁₃, Y₂=X_(π(2))=X₁₁, . . . ,Y₄₃=X_(π(43))=X₁, and Y₄₄=X_(π(44))=X₃₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 20^(th) bit group to the 0^(th) bitgroup, the 13^(th) bit group to the 1^(st) bit group, the 11^(th) bitgroup to the 2^(nd) bit group, . . . , the 1^(st) bit group to the43^(rd) bit group, and the 38^(th) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 9/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 17 presented below. In particular, table 17 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 7

TABLE 17 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block 17 8 7 5 31 4 16 13 23 25 14 3 920 15 18 11 24 22 19 10 12 37 of Group-wise 40 39 44 30 35 41 34 26 43 628 38 33 2 32 36 0 27 29 42 1 21 interleaver input

In the case of Table 17, Equation 21 may be expressed asY₀=X_(π(0))=X₁₇, Y₁=X_(π(1))=X₈, Y₂=X_(π(2))=X₇, . . . ,Y₄₃=X_(π(43))=X₁, and Y₄₄=X_(π(44))=X₂₁. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 17^(th) bit group to the 0^(th) bitgroup, the 8^(th) bit group to the 1^(st) bit group, the 7^(th) bitgroup to the 2^(nd) bit group, . . . , the 1^(st) bit group to the43^(rd) bit group, and the 21^(st) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 11/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 18 presented below. In particular, table 18 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 9

TABLE 18 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block 21 23 5 6 27 29 2 25 4 12 26 3211 8 9 19 28 14 10 20 13 18 37 of Group-wise 43 34 36 39 38 22 40 35 4233 0 17 24 31 1 7 3 41 44 15 16 30 interleaver input

In the case of Table 18, Equation 21 may be expressed asY₀=X_(π(0))=X₂₁, Y₁=X_(π(1))=X₂₃, Y₂=X_(π(2))=X₅, . . . ,Y₄₃=X_(π(43))=X₁₆, Y₄₄=X_(π(44))=X₃₀. Accordingly, the group interleaver122 may rearrange the order of the plurality of bit groups in bit groupwise by changing the 21^(st) bit group to the 0^(th) bit group, the23^(rd) bit group to the 1^(st) bit group, the 5^(th) bit group to the2^(nd) bit group, . . . , the 16^(th) bit group to the 43^(rd) bitgroup, and the 30^(th) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 13/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 19 presented below. In particular, table 19 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 11

TABLE 19 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block 4 13 8 15 6 14 11 10 9 7 12 26 310 20 17 23 30 21 25 29 1 40 of Group-wise 39 2 5 43 18 3 16 41 42 44 3728 32 22 35 33 36 27 19 34 24 38 interleaver input

In the case of Table 19, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₁₃, Y₂=X_(π(2))=X₈, . . . , Y₄₃=X_(π(43))=X₂₄, andY₄₄=X_(π(44))=X₃₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 13^(th) bit group tothe 1^(st) bit group, the 8^(th) bit group to the 2^(nd) bit group . . .24^(th) bit group to the 43^(rd) bit group, and the 38^(th) bit group tothe 44^(th) bit group, . . . , .

In another example, when the length of the LDPC codeword is 16200, thecode rate is 5/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 20 presented below. In particular, table 20 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 4.

TABLE 20 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block 5 20 9 12 11 18 7 14 6 4 13 16 3531 41 10 2 27 1 8 3 38 21 of Group-wise 33 23 43 19 37 28 25 30 24 22 1734 44 32 15 36 42 40 0 26 39 29 interleaver input

In the case of Table 20, Equation 21 may be expressed as Y₀=X_(π(0))=X₅,Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₉, . . . , Y₄₃=X_(π(43))=X₃₉, andY₄₄=X_(π(44))=X₂₉. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 5^(th) bit group to the 0^(th) bit group, the 20^(th) bit group tothe 1^(st) bit group, the 9^(th) bit group to the 2^(nd) bit group, . .. , the 39^(th) bit group to the 43^(rd) bit group, and the 29^(th) bitgroup to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 7/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 21 presented below. In particular, table 21 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 6.

TABLE 21 Order of bits group to be block interleaved π(j) (0 ≤ j < 45)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 18 16 3 0 19 15 2 5 8 10 4 4344 33 7 20 12 14 40 6 17 35 29 Group-wise 3 31 41 42 39 25 22 24 26 9 2837 23 32 30 11 21 1 36 27 34 38 interleaver input

In the case of Table 21, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆, Y₂=X_(π(2))=X₁₃, . . . ,Y₄₃=X_(π(43))=X₃₄, and Y₄₄=X_(π(44))=X₃₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing, the 18^(th) bit group to the 0^(th) bitgroup, the 16^(th) bit group to the 1^(st) bit group, the 13^(th) bitgroup to the 2^(nd) bit group, . . . , the 34^(th) bit group to the43^(rd) bit group, and the 38^(th) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 9/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 22 presented below. In particular, table 22 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 8.

TABLE 22 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 20 14 13 6 31 24 10 18 21 1725 34 12 2 22 23 16 0 11 5 26 19 8 Group-wise 1 38 4 3 9 7 15 39 32 4235 27 29 36 28 41 40 37 30 33 43 44 interleaver input

In the case of Table 22, Equation 21 may be expressed asY₀=X_(π(0))=X₂₀, Y₁=X_(π(1))=X₁₄, Y₂=X_(π(2))=X₁₃, . . . ,Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 20^(th) bit group to the 0^(th) bitgroup, the 14^(th) bit group to the 1^(st) bit group, the 13^(th) bitgroup to the 2^(nd) bit group, . . . , the 43^(rd) bit group to the43^(rd) bit group, and the 44^(th) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 11/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 23 presented below. In particular, table 23 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 10.

TABLE 23 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 15 10 5 2 0 25 22 11 1 7 21 1913 24 16 23 26 14 20 29 18 12 38 Group-wise 34 33 39 40 32 36 44 37 35 43 9 41 17 28 42 27 43 6 8 30 31 interleaver input

In the case of Table 23, Equation 21 may be expressed asY₀=X_(π(0))=X₁₅, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₅, . . . ,Y₄₃=X_(π(43))=X₃₀, Y₄₄=X_(π(44))=X₃₁. Accordingly, the group interleaver122 may rearrange the order of the plurality of bit groups in bit groupwise by changing the 15^(th) bit group to the 0^(th) bit group, the10^(th) bit group to the 1^(st) bit group, the 5th bit group to the2^(nd) bit group, . . . , the 30^(th) bit group to the 43^(rd) bitgroup, and the 31^(st) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 13/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 24 presented below. In particular, table 24 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 12.

TABLE 24 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 4 11 1 5 9 8 7 6 19 15 2 21 1012 17 16 13 18 31 14 20 25 40 Group-wise 24 42 0 3 23 22 44 43 41 39 2633 38 35 36 30 37 32 34 27 28 29 interleaver input

In the case of Table 24, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₁₁, Y₂=X_(π(2))=X₁, . . . , Y₄₃=X_(π(43))=X₂₈,Y₄₄=X_(π(44))=X₂₉. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 11^(th) bit group tothe 1^(st) bit group, the 1^(st) bit group to the 2^(nd) bit group, . .. , the 28^(th) bit group to the 43^(rd) bit group, and the 29^(th) bitgroup to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 7/15, and the modulation method is 256-QAM, π(j) may bedefined as in table 25 presented below. In particular, table 25 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 6.

TABLE 25 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 39 18 33 25 8 14 7 4 11 10 543 20 30 6 22 12 0 41 9 2 17 40 Group-wise 36 31 15 42 16 29 19 1 26 3528 37 21 24 23 13 38 3 32 27 34 44 interleaver input

In the case of Table 25, Equation 21 may be expressed asY₀=X_(π(0))=X₃₉, Y₁=X_(π(1))=X₁₈, Y₂=X_(π(2))=X₃₃, . . . ,Y₄₃=X_(π(43))=X₃₄, Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver122 may rearrange the order of the plurality of bit groups in bit groupwise by changing, the 39^(th) bit group to the 0^(th) bit group, the18^(th) bit group to the 1^(st) bit group, the 33^(th) bit group to the2^(nd) bit group, . . . , the 34^(th) bit group to the 43^(rd) bitgroup, and the 44^(th) bit group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 9/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 26 presented below. In particular, table 26 may beapplied when LDPC encoding is performed based on the parity check matrixdefined by table 7.

TABLE 26 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 17 8 7 13 31 4 3 19 23 25 5 169 20 15 18 11 24 22 14 10 6 37 Group-wise 40 39 44 30 35 41 34 26 43 1228 38 33 2 32 36 0 27 29 42 1 21 interleaver input

In the case of Table 26, Equation 21 may be expressed asY₀=X_(π(0))=X₁₇, Y₁=X_(π(1))=X₈, Y₂=X_(π(2))=X₇, . . . ,Y₄₃=X_(π(43))=X₁, Y₄₄=X_(π(44))=X₂₁. Accordingly, the group interleaver122 may rearrange the order of the plurality of bit groups in bit groupwise by changing the 17^(th) bit group to the 0^(th) bit group, the8^(th) bit group to the 1^(st) bit group, the 7^(th) bit group to the2^(nd) bit group, . . . , the 1^(st) bit group to the 43^(rd) bit group,and the 21^(st) it group to the 44^(th) bit group.

In another example, when the length of the LDPC codeword is 16200, thecode rate is 9/15, and the modulation method is 16-QAM, π(j) may bedefined as in table 27 presented below. In particular, table 27 may beapplied when LDPC encoding, is performed based on the parity checkmatrix defined by table 8.

TABLE 27 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 interleaver output π(j)-th block of 4 14 13 6 30 24 39 20 5 10 2534 15 21 22 9 16 0 11 7 12 19 8 Group-wise 1 18 2 44 26 31 23 38 37 4235 41 29 36 28 17 27 40 33 32 43 3 interleaver input

In the case of Table 27, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₁₄, Y₂=X_(π(2))=X₁₃, . . . , Y₄₃=X_(π(43))=X₄₃,Y₄₄=X_(π(44))=X₃. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 14^(th) bit group tothe 1^(st) bit group, the 13^(th) bit group to the 2^(nd) bit group, . .. , the 43^(rd) bit group to the 43^(rd) bit group, and the 3^(rd) bitgroup to the 44^(th) bit group.

In the above-described examples, the length of the LDPC codeword is16200 and the code rate is 5/15, 7/15, 9/15, 11/15, and 13/15. However,this is merely an example and the interleaving pattern may be definedvariously when the length of the LDPC codeword is 64800 or the code ratehas different values.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bit group wise by using Equation 21 andTables 15 to 27.

“j-th block of Group-wise Interleaver output” in tables 15 to 27indicates the j-th bit group output from the group interleaver 122 afterinterleaving, and “π(j)-th block of Group-wise Interleaver input”indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bit group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bit groups to be blockinterleaved” is set forth in Tables 15 to 27 in relation to π(j).

The LDPC codeword which is group-interleaved in the above-describedmethod is illustrated in FIG. 25 . Comparing the LDPC codeword of FIG.25 and the LDPC codeword of FIG. 24 before group interleaving, it can beseen that the order of the plurality of bit groups constituting the LDPCcodeword is rearranged.

That is, as shown in FIGS. 24 and 25 , the groups of the LDPC codewordare arranged in order of bit group X₀, bit group X₁, . . . , bit groupX_(Ngroup−1) before being group-interleaved, and are arranged in anorder of bit group Y₀, bit group Y₁, . . . , bit group Y_(Ngroup−1)after being group-interleaved. In this case, the order of arranging thebit groups by the group interleaving may be determined based on Tables15 to 27.

The group twist interleaver 123 interleaves bits in a same group. Thatis, the group twist interleaver 123 may rearrange the order of the bitsin the same bit group by changing the order of the bits in the same bitgroup.

In this case, the group twist interleaver 123 may rearrange the order ofthe bits in the same bit group by cyclic-shifting a predetermined numberof bits from among the bits in the same bit group.

For example, as shown in FIG. 26 , the group twist interleaver 123 maycyclic-shift bits included in the bit group Y₁ to the right by 1 bit. Inthis case, the bits located in the 0^(th) position, the 1^(st) position,the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th)position in the bit group Y₁ as shown in FIG. 26 are cyclic-shifted tothe right by 1 bit. As a result, the bit located in the 359^(th)position before being cyclic-shifted is located in the front of the bitgroup Y₁ and the bits located in the 0^(th) position, the 1^(st)position, the 2^(nd) position, . . . , the 358^(th) position beforebeing cyclic-shifted are shifted to the right serially by 1 bit andlocated.

In addition, the group twist interleaver 123 may rearrange the order ofbits in each bit group by cyclic-shifting a different number of bits ineach bit group.

For example, the group twist interleaver 123 may cyclic-shift the bitsincluded in the bit group Y₁ to the right by 1 bit, and may cyclic-shiftthe bits included in the bit group Y₂ to the right by 3 bits.

However, the above-described group twist interleaver 123 may be omittedaccording to circumstances.

In addition, the group twist interleaver 123 is placed after the groupinterleaver 122 in the above-described example. However, this is merelyan example. That is, the group twist interleaver 123 changes only theorder of bits in a certain bit group and does not change the order ofthe bit groups. Therefore, the group twist interleaver 123 may be placedbefore the group interleaver 122.

The block interleaver 124 interleaves the plurality of bit groups theorder of which has been rearranged. Specifically, the block interleaver124 may interleave the plurality of bit groups the order of which hasbeen rearranged by the group interleaver 122 in bit group wise (or bitsgroup unit). The block interleaver 124 is formed of a plurality ofcolumns each including a plurality of rows and may interleave bydividing the plurality of rearranged bit groups based on a modulationorder determined according to a modulation method.

In this case, the block interleaver 124 may interleave the plurality ofbit groups the order of which has been rearranged by the groupinterleaver 122 in bit group wise. Specifically, the block interleaver124 may interleave by dividing the plurality of rearranged bit groupsaccording to a modulation order by using a first part and a second part.

Specifically, the block interleaver 124 interleaves by dividing each ofthe plurality of columns into a first part and a second part, writingthe plurality of bit groups in the plurality of columns of the firstpart serially in bit group wise, dividing the bits of the other bitgroups into groups (or sub bit groups) each including a predeterminednumber of bits based on the number of columns, and writing the sub bitgroups in the plurality of columns of the second part serially.

Herein, the number of bit groups which are interleaved in bit group wisemay be determined by at least one of the number of rows and columnsconstituting the block interleaver 124, the number of bit groups and thenumber of bits included in each bit group. In other words, the blockinterleaver 124 may determine the bit groups which are to be interleavedin bit group wise considering at least one of the number of rows andcolumns constituting the block interleaver 124, the number of bit groupsand the number of bits included in each bit group, interleave thecorresponding bit groups in bit group wise, and divide bits of the otherbit groups into sub bit groups and interleave the sub bit groups. Forexample, the block interleaver 124 may interleave at least part of theplurality of bit groups in bit group wise using the first part, anddivide bits of the other bit groups into sub bit groups and interleavethe sub bit groups using the second part.

Meanwhile, interleaving bit groups in bit group wise means that the bitsincluded in the same bit group are written in the same column. In otherwords, the block interleaver 124, in case of bit groups which areinterleaved in bit group wise, may not divide the bits included in thesame bit groups and write the bits in the same column, and in case ofbit groups which are not interleaved in bit group wise, may divide thebits in the bit groups and write the bits in different columns.

Accordingly, the number of rows constituting the first part is amultiple of the number of bits included in one bit group (for example,360), and the number of rows constituting the second part may be lessthan the number of bits included in one bit group.

In addition, in all bit groups interleaved by the first part, the bitsincluded in the same bit group are written and interleaved in the samecolumn of the first part, and in at least one group interleaved by thesecond part, the bits are divided and written in at least two columns ofthe second part.

The specific interleaving method will be described later.

Meanwhile, the group twist interleaver 123 changes only the order ofbits in the bit group and does not change the order of bit groups byinterleaving. Accordingly, the order of the bit groups to beblock-interleaved by the block interleaver 124, that is, the order ofthe bit groups to be input to the block interleaver 124, may bedetermined by the group interleaver 122. Specifically, the order of thebit groups to be block-interleaved by the block interleaver 124 may bedetermined by π(j) defined in Tables 15 to 27.

As described above, the block interleaver 124 may interleave theplurality of bit groups the order of which has been rearranged in bitgroup wise by using the plurality of columns each including theplurality of rows.

In this case, the block interleaver 124 may interleave the LDPC codewordby dividing the plurality of columns into at least two parts. Forexample, the block interleaver 124 may divide each of the plurality ofcolumns into the first part and the second part and interleave theplurality of bit groups constituting the LDPC codeword.

In this case, the block interleaver 124 may divide each of the pluralityof columns into N number of parts (N is an integer greater than or equalto 2) according to whether the number of bit groups constituting theLDPC codeword is an integer multiple of the number of columnsconstituting the block interleaver 124, and may perform interleaving.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns constituting the blockinterleaver 124, the block interleaver 124 may interleave the pluralityof bit groups constituting the LDPC codeword in bit group wise withoutdividing each of the plurality of columns into parts.

Specifically, the block interleaver 124 may interleave by writing theplurality of bit groups of the LDPC codeword on each of the columns inbit group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbit group wise in a row direction.

In this case, the block interleaver 124 may interleave by writing bitsincluded in a predetermined number of bit groups, which corresponds to aquotient obtained by dividing the number of bit groups of the LDPCcodeword by the number of columns of the block interleaver 124, on eachof the plurality of columns serially in a column direction, and readingeach row of the plurality of columns in which the bits are written in arow direction.

Hereinafter, the group located in the j^(th) position after beinginterleaved by the group interleaver 122 will be referred to as groupY_(j).

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups and the number of bit groups N_(group) is a multiple of C.

In this case, when the quotient obtained by dividing N_(group) number ofbit groups constituting the LDPC codeword by C number of columnsconstituting the block interleaver 124 is A (=N_(group)/C) (A is aninteger greater than 0), the block interleaver 124 may interleave bywriting A (=N_(group)/C) number of bit groups on each column serially ina column direction and reading bits written on each column in a rowdirection.

For example, as shown in FIG. 27 , the block interleaver 124 writes bitsincluded in bit group Y₀, bit group Y₁, . . . , bit group Y_(A−1) in the1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bitsincluded in bit group Y_(A), bit group Y_(A+1), . . . , bit groupY_(2A−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . .. , and writes bits included in bit group Y_(CA−A), bit groupY_(CA−A+1), . . . , bit group Y_(CA−1) in the column C from the 1^(st)row to the R₁ ^(th) row. The block interleaver 124 may read the bitswritten in each row of the plurality of columns in a row direction.

Accordingly, the block interleaver 124 interleaves all bit groupsconstituting the LDPC codeword in bit group wise.

However, when the number of bit groups of the LDPC codeword is not aninteger multiple of the number of columns of the block interleaver 124,the block interleaver 124 may divide each column into 2 parts andinterleave a part of the plurality of bit groups of the LDPC codeword inbit group wise, and divide bits of the other bit groups into sub bitgroups and interleave the sub bit groups. In this case, the bitsincluded in the other bit groups, that is, the bits included in thenumber of groups which correspond to the remainder when the number ofbit groups constituting the LDPC codeword is divided by the number ofcolumns are not interleaved in bit group wise, but interleaved by beingdivided according to the number of columns.

Specifically, the block interleaver 124 may interleave the LDPC codewordby dividing each of the plurality of columns into two parts.

In this case, the block interleaver 124 may divide the plurality ofcolumns into the first part and the second part based on at least one ofthe number of columns of the block interleaver 124, the number of bitgroups of the LDPC codeword, and the number of bits of bit groups.

Here, each of the plurality of bit groups may be formed of 360 bits. Inaddition, the number of bit groups of the LDPC codeword is determinedbased on the length of the LDPC codeword and the number of bits includedin the bit group. For example, when an LDPC codeword in the length of16200 is divided such that each bit group has 360 bits, the LDPCcodeword is divided into 45 bit groups. Alternatively, when an LDPCcodeword in the length of 64800 is divided such that each bit group has360 bits, the LDPC codeword may be divided into 180 bit groups. Further,the number of columns constituting the block interleaver 124 may bedetermined according to a modulation method. This will be explained indetail below.

Accordingly, the number of rows constituting each of the first part andthe second part may be determined based on the number of columnsconstituting the block interleaver 124, the number of bit groupsconstituting the LDPC codeword, and the number of bits constituting eachof the plurality of bit groups.

Specifically, in each of the plurality of columns, the first part may beformed of as many rows as the number of bits included in at least onebit group which can be written in each column in bit group wise fromamong the plurality of bit groups of the LDPC codeword, according to thenumber of columns constituting the block interleaver 124, the number ofbit groups constituting the LDPC codeword, and the number of bitsconstituting each bit group.

In each of the plurality of columns, the second part may be formed ofrows excluding as many rows as the number of bits included in at leastsome bit groups which can be written in each of the plurality of columnsin bit group wise. Specifically, the number rows of the second part maybe the same value as a quotient when the number of bits included in allbit groups excluding bit groups corresponding to the first part isdivided by the number of columns constituting the block interleaver 124.In other words, the number of rows of the second part may be the samevalue as a quotient when the number of bits included in the remainingbit groups which are not written in the first part from among bit groupsconstituting the LDPC codeword is divided by the number of columns.

That is, the block interleaver 124 may divide each of the plurality ofcolumns into the first part including as many rows as the number of bitsincluded in bit groups which can be written in each column in bit groupwise, and the second part including the other rows.

Accordingly, the first part may be formed of as many rows as the numberof bits included in bit groups, that is, as many rows as an integermultiple of M. However, since the number of codeword bits constitutingeach bit group may be an aliquot part of M as described above, the firstpart may be formed of as many rows as an integer multiple of the numberof bits constituting each bit group.

In this case, the block interleaver 124 may interleave by writing andreading the LDPC codeword in the first part and the second part in thesame method.

Specifically, the block interleaver 124 may interleave by writing theLDPC codeword in the plurality of columns constituting each of the firstpart and the second part in a column direction, and reading theplurality of columns constituting the first part and the second part inwhich the LDPC codeword is written in a row direction.

That is, the block interleaver 124 may interleave by writing the bitsincluded in at least some bit groups which can be written in each of theplurality of columns in bit group wise in each of the plurality ofcolumns of the first part serially, dividing the bits included in theother bit groups except the at least some bit groups and writing in eachof the plurality of columns of the second part in a column direction,and reading the bits written in each of the plurality of columnsconstituting each of the first part and the second part in a rowdirection.

In this case, the block interleaver 124 may interleave by dividing theother bit groups except the at least some bit groups from among theplurality of bit groups based on the number of columns constituting theblock interleaver 124.

Specifically, the block interleaver 124 may interleave by dividing thebits included in the other bit groups by the number of a plurality ofcolumns, writing each of the divided bits in each of a plurality ofcolumns constituting the second part in a column direction, and readingthe plurality of columns constituting the second part, where the dividedbits are written, in a row direction.

That is, the block interleaver 124 may divide the bits included in theother bit groups except the bit groups written in the first part fromamong the plurality of bit groups of the LDPC codeword, that is, thebits in the number of bit groups which correspond to the remainder whenthe number of bit groups constituting the LDPC codeword is divided bythe number of columns, by the number of columns, and may write thedivided bits in each column of the second part serially in a columndirection.

In this case, the block interleaver 124 may interleave by dividing theother bit groups except the at least some bit groups from among theplurality of bit groups based on the number of columns constituting theblock interleaver 124.

To be specific, the block interleaver 124 may interleave by dividing thebits included in the reminder bit groups by the number of a plurality ofcolumns, writing each of the divided bits in each of a plurality ofcolumns constituting the second part in a column direction, and readingthe plurality of columns constituting the second part, where the dividedbits are written in a row direction.

That is, the block interleaver 124 may divide the bits included in theother bit groups except the bit groups written in the first part fromamong the plurality of bit groups constituting the LDPC codeword, thatis, the bits in the number of bit groups which correspond to theremainder when the number of bit groups constituting the LDPC codewordis divided by the number of columns, and may write the divided bits ineach column of the second part serially in a column direction.

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups, the number of bit groups N_(group) is not a multiple of C, andA×C+1=N_(group) (A is an integer greater than 0). In other words, it isassumed that when the number of bit groups constituting the LDPCcodeword is divided by the number of columns, the quotient is A and theremainder is 1.

In this case, as shown in FIGS. 28 and 29 , the block interleaver 124may divide each column into a first part including R₁ number of rows anda second part including R₂ number of rows. In this case, R₁ maycorrespond to the number of bits included in bit groups which can bewritten in each column in bit group wise, and R₂ may be R₁ subtractedfrom the number of rows of each column.

That is, in the above-described example, the number of bit groups whichcan be written in each column in bit group wise is A, and the first partof each column may be formed of as many rows as the number of bitsincluded in A number of bit groups, that is, may be formed of as manyrows as A×M number.

In this case, the block interleaver 124 writes the bits included in thebit groups which can be written in each column in bit group wise, thatis, A number of bit groups, in the first part of each column in thecolumn direction.

That is, as shown in FIGS. 28 and 29 , the block interleaver 124 writesthe bits included in each of bit group Y₀, bit group Y₁, . . . , groupY_(A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st)column, writes bits included in each of bit group Y_(A), bit groupY_(A+1), . . . , bit group Y_(2A−1) in the 1^(st) to R₁ ^(th) rows ofthe first part of the 2^(nd) column, . . . , writes bits included ineach of bit group Y_(CA−A), bit group Y_(CA−A+1), . . . , bit groupY_(CA−1) in the 1^(st) to R₁ ^(th) rows of the first part of the columnC.

As described above, the block interleaver 124 writes the bits includedin the bit groups which can be written in each column in bit group wisein the first part of each column.

In other words, in the above exemplary embodiment, the bits included ineach of bit group (Y₀), bit group (Y₁), . . . , bit group (Y_(A−1)) maynot be divided and all of the bits may be written in the first column,the bits included in each of bit group (Y_(A)), bit group (Y_(A+1)), . .. , bit group (Y_(2A−1)) may not be divided and all of the bits may bewritten in the second column, and the bits included in each of bit group(Y_(CA−A)), bit group (Y_(CA−A+1)), . . . , group (Y_(CA−1)) may not bedivided and all of the bits may be written in the C column. As such, allbit groups interleaved by the first part are written in the same columnof the first part.

Thereafter, the block interleaver 124 divides bits included in the otherbit groups except the bit groups written in the first part of eachcolumn from among the plurality of bit groups, and writes the bits inthe second part of each column in the column direction. In this case,the block interleaver 124 divides the bits included in the other bitgroups except the bit groups written in the first part of each column bythe number of columns, so that the same number of bits are written inthe second part of each column, and writes the divided bits in thesecond part of each column in the column direction.

In the above-described example, since A×C+1=N_(group), when the bitgroups constituting the LDPC codeword are written in the first partserially, the last bit group Y_(Ngroup−1) of the LDPC codeword is notwritten in the first part and remains. Accordingly, the blockinterleaver 124 divides the bits included in the bit group Y_(Ngroup−1)into C number of sub bit groups as shown in FIG. 28 , and writes thedivided bits (that is, the bits corresponding to the quotient when thebits included in the last group (Y_(Ngroup−1)) are divided by C) in thesecond part of each column serially.

The bits divided based on the number of columns may be referred to assub bit groups. In this case, each of the sub bit groups may be writtenin each column of the second part. That is, the bits included in the bitgroups may be divided and may form the sub bit groups.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂^(th) rows of the second part of the 1^(st) column, writes the bits inthe 1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . .. , and writes the bits in the 1^(st) to R₂ ^(th) rows of the secondpart of the column C. In this case, the block interleaver 124 may writethe bits in the second part of each column in the column direction asshown in FIG. 28 .

That is, in the second part, the bits constituting the bit group may notbe written in the same column and may be written in the plurality ofcolumns. In other words, in the above example, the last bit group(Y_(Ngroup−1)) is formed of M number of bits and thus, the bits includedin the last bit group (Y_(Ngroup−1)) may be divided by M/C and writtenin each column. That is, the bits included in the last bit group(Y_(Ngroup−1)) are divided by M/C, forming M/C number of sub bit groups,and each of the sub bit groups may be written in each column of thesecond part.

Accordingly, in at least one bit group which is interleaved by thesecond part, the bits included in the at least one bit group are dividedand written in at least two columns constituting the second part.

In the above-described example, the block interleaver 124 writes thebits in the second part in the column direction. However, this is merelyan example. That is, the block interleaver 124 may write the bits in theplurality of columns of the second part in the row direction. In thiscase, the block interleaver 124 may write the bits in the first part inthe same method as described above.

Specifically, referring to FIG. 29 , the block interleaver 124 writesthe bits from the 1^(st) row of the second part in the 1^(st) column tothe 1^(st) row of the second part in the column C, writes the bits fromthe 2^(nd) row of the second part in the 1^(st) column to the 2^(nd) rowof the second part in the column C, . . . , etc., and writes the bitsfrom the R₂ ^(th) row of the second part in the 1^(st) column to the R₂^(th) row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written ineach row of each part serially in the row direction. That is, as shownin FIGS. 28 and 29 , the block interleaver 124 reads the bits written ineach row of the first part of the plurality of columns serially in therow direction, and reads the bits written in each row of the second partof the plurality of columns serially in the row direction.

Accordingly, the block interleaver 124 may interleave a part of theplurality of bit groups constituting the LDPC codeword in bit groupwise, and divide and interleave some of the remaining bit groups. Thatis, the block interleaver 124 may interleave by writing the LDPCcodeword constituting a predetermined number of bit groups from amongthe plurality of bit groups in the plurality of columns of the firstpart in bit group wise, dividing the bits of the other bit groups andwriting the bits in each of the columns of the second part, and readingthe plurality of columns of the first and second parts in the rowdirection.

As described above, the block interleaver 124 may interleave theplurality of bit groups in the methods described above with reference toFIGS. 27 to 29 .

In particular, in the case of FIG. 28 , the bits included in the bitgroup which does not belong to the first part are written in the secondpart in the column direction and read in the row direction. In view ofthis, the order of the bits included in the bit group which does notbelong to the first part is rearranged. Since the bits included in thebit group which does not belong to the first part are interleaved asdescribed above, bit error rate (BER)/frame error rate (FER) performancecan be improved in comparison with a case in which such bits are notinterleaved.

However, the bit group which does not belong to the first part may notbe interleaved as shown in FIG. 29 . That is, since the blockinterleaver 124 writes and reads the bits included in the group whichdoes not belong to the first part in and from the second part in the rowdirection, the order of the bits included in the group which does notbelong to the first part is not changed and the bits are output to themodulator 130 serially. In this case, the bits included in the groupwhich does not belong to the first part may be output serially andmapped onto a modulation symbol.

In FIGS. 28 and 29 , the last single bit group of the plurality of bitgroups is written in the second part. However, this is merely anexample. The number of bit groups written in the second part may varyaccording to the total number of bit groups of the LDPC codeword, thenumber of columns and rows, the number of transmission antennas, etc.

The block interleaver 124 may have a configuration as shown in tables 28and 29 presented below:

TABLE 28 N_(ldpc) = 64800 QPSK 16 QAM 64 QAM 256 QAM 1024 QAM 4096 QAM C2 4 6 8 10 12 R₁ 32400 16200 10800 7920 6480 5400 R₂ 0 0 0 180 0 0

TABLE 29 N_(ldpc) = 16200 QPSK 16 QAM 64 QAM 256 QAM 1024 QAM 4096 QAM C2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or N_(C)) is the number of columns of the block interleaver124, R₁ is the number of rows constituting the first part in eachcolumn, and R₂ is the number of rows constituting the second part ineach column.

Referring to Tables 28 and 29, the number of columns has the same valueas a modulation order according to a modulation method, and each of aplurality of columns is formed of rows corresponding to the number ofbits constituting the LDPC codeword divided by the number of a pluralityof columns.

For example, when the length N_(ldpc) of the LDPC codeword is 16200 andthe modulation method is 16-QAM, the block interleaver 124 is formed of4 columns as the modulation order is 4 in the case of 16-QAM, and eachcolumn is formed of rows as many as R₁+R₂=4050(=16200/4).

Meanwhile, referring to Tables 28 and 29, when the number of bit groupsconstituting an LDPC codeword is an integer multiple of the number ofcolumns, the block interleaver 124 interleaves without dividing eachcolumn. Therefore, R₁ corresponds to the number of rows constitutingeach column, and R₂ is 0. In addition, when the number of bit groupsconstituting an LDPC codeword is not an integer multiple of the numberof columns, the block interleaver 124 interleaves the groups by dividingeach column into the first part formed of R₁ number of rows, and thesecond part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to thenumber of bits constituting a modulation symbol, bits included in a samebit group are mapped onto a single bit of each modulation symbol asshown in Tables 28 and 29.

For example, when N_(ldpc)=16200 and the modulation method is 16-QAM,the block interleaver 124 may be formed of four (4) columns eachincluding 4050 rows. In this case, the bits included in each of theplurality of bit groups are written in the four (4) columns and the bitswritten in the same row in each column are output serially. In thiscase, since four (4) bits constitute a single modulation symbol in themodulation method of 256-QAM, bits included in the same bit group, thatis, bits output from a single column, may be mapped onto a single bit ofeach modulation symbol. For example, bits included in a bit groupwritten in the 1^(st) column may be mapped onto the first bit of eachmodulation symbol.

Referring to Tables 28 and 29, the total number of rows of the blockinterleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, R₁, is an integermultiple of the number of bits included in each group, M (e.g., M=360),and maybe expressed as └N_(group)/C┘×M and the number of rows of thesecond part, R₂, may be N_(ldpc)/C−R₁. Herein, └N_(group)/C┘ is thelargest integer below N_(group)/C. Since R₁ is an integer multiple ofthe number of bits included in each group, M, bits may be written in R₁in bit groups wise.

In addition, when the number of bit groups of the LDPC codeword is not amultiple of the number of columns, it can be seen from Tables 28 and 29that the block interleaver 124 interleaves by dividing each column intotwo parts.

Specifically, the length of the LDPC codeword divided by the number ofcolumns is the total number of rows included in the each column. In thiscase, when the number of bit groups of the LDPC codeword is a multipleof the number of columns, each column is not divided into two parts.However, when the number of bit groups of the LDPC codeword is not amultiple of the number of columns, each column is divided into twoparts.

For example, it is assumed that the number of columns of the blockinterleaver 124 is identical to the number of bits constituting amodulation symbol, and an LDPC codeword is formed of 64800 bits as shownin Table 28. In this case, each bit group of the LDPC codeword is formedof 360 bits, and the LDPC codeword is formed of 64800/360(=180) bitgroups.

When the modulation method is 16-QAM, the block interleaver 124 may beformed of four (4) columns and each column may have 64800/4(=16200)rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/4(=45), bits can be written ineach column in bit group wise without dividing each column into twoparts. That is, bits included in 45 bit groups which is the quotientwhen the number of bit groups constituting the LDPC codeword is dividedby the number of columns, that is, 45×360(=16200) bits can be written ineach column.

However, when the modulation method is 256-QAM, the block interleaver124 may be formed of eight (8) columns and each column may have64800/8(=8100) rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/8=22.5, the number of bit groupsconstituting the LDPC codeword is not an integer multiple of the numberof columns. Accordingly, the block interleaver 124 divides each of theeight (8) columns into two parts to perform interleaving in bit groupwise.

In this case, since the bits should be written in the first part of eachcolumn in bit group wise, the number of bit groups which can be writtenin the first part of each column in bit group wise is 22, which is thequotient when the number of bit groups constituting the LDPC codeword isdivided by the number of columns, and accordingly, the first part ofeach column has 22×360(=7920) rows. Accordingly, 7920 bits included in22 bit groups may be written in the first part of each column.

The second part of each column has rows which are the rows of the firstpart subtracted from the total rows of each column. Accordingly, thesecond part of each column includes 8100−7920(=180) rows.

In this case, the bits included in the other bit groups which have notbeen written in the first part are divided and written in the secondpart of each column.

Specifically, since 22×8(=176) bit groups are written in the first part,the number of bit groups to be written in the second part is 180−176(=4) (for example, bit group Y₁₇₆, bit group Y₁₇₇, bit group Y₁₇₉ fromamong bit group Y₀, bit group Y₁, bit group Y₂, . . . , constituting theLDPC codeword).

Accordingly, the block interleaver 124 may write the four (4) bit groupswhich have not been written in the first part and remains from among thegroups constituting the LDPC codeword in the second part of each columnserially.

That is, the block interleaver 124 may write 180 bits of the 360 bitsincluded in the bit group Y₁₇₆ in the 1^(st) row to the 180^(th) row ofthe second part of the 1^(st) column in the column direction, and maywrite the other 180 bits in the 1^(st) row to the 180^(th) row of thesecond part of the 2^(nd) column in the column direction. In addition,the block interleaver 124 may write 180 bits of the 360 bits included inthe bit group Y₁₇₇ in the 1^(st) row to the 180^(th) row of the secondpart of the 3^(rd) column in the column direction, and may write theother 180 bits in the 1^(st) row to the 180^(th) row of the second partof the 4^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₈ in the 1^(st) row to the 180^(th) row of the second part ofthe 5^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the6^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₉ in the 1^(st) row to the 180^(th) row of the second part ofthe 7^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the8^(th) column in the column direction.

Accordingly, the bits included in the bit group which has not beenwritten in the first part and remains are not written in the same columnin the second part and may be divided and written in the plurality ofcolumns.

Hereinafter, the block interleaver 124 of FIG. 23 according to anexemplary embodiment will be explained in detail with reference to FIG.30 .

In a group-interleaved LDPC codeword (v₀, v₁, . . . , v_(N) _(ldpc) ⁻¹),Y_(j) is continuously arranged like V={Y₀, Y₁, . . . Y_(N) _(group) ⁻¹}.

The LDPC codeword after group interleaving may be interleaved by theblock interleaver 124 as shown in FIG. 30 . In this case, the blockinterleaver 124 divide a plurality of columns into the first part(Part 1) and the second part (Part 2) based on the number of columns ofthe block interleaver 124 and the number of bits of bit groups. In thiscase, in the first part, the bits constituting the bit groups may bewritten in the same column, and in the second part, the bitsconstituting the bit groups may be written in a plurality of columns.

Specifically, input bits vi are written serially from the first part tothe second part column wise, and then read out serially from the firstpart to the second part row wise. That is, the data bits v_(i) arewritten serially into the block interleaver column-wise starting in thefirst part and continuing column-wise finishing in the second part, andthen read out serially row-wise from the first part and then row-wisefrom the second part. Accordingly, the bit included in the same bitgroup in the first part may be mapped onto a single bit of eachmodulation symbol.

In this case, the number of columns and the number of rows of the firstpart and the second part of the block interleaver 124 vary according toa modulation format and a length of the LDPC codeword as in Table 30presented below. That is, the first part and the second part blockinterleaving configurations for each modulation format and code lengthare specified in Table 30 presented below. Herein, the number of columnsof the block interleaver 124 may be equal to the number of bitsconstituting a modulation symbol. In addition, a sum of the number ofrows of the first part, N_(r1) and the number of rows of the secondpart, N_(r2), is equal to N_(ldpc)/N_(C) (herein, N_(C) is the number ofcolumns). In addition, since N_(r1)(=└N_(group)/N_(c)┘×360) is amultiple of 360, a multiple of bit groups may be written in the firstpart.

TABLE 30 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) Modulation N_(ldpc)= 64800 N_(ldpc) = 16200 N_(ldpc) = 64800 N_(ldpc) = 16200 Columns N_(c)QPSK 32400 7920 0 180 2 16-QAM 16200 3960 0 90 4 64-QAM 10800 2520 0 1806 256-QAM 7920 1800 180 225 8 1024-QAM 6480 1440 0 180 10 4096-QAM 54001080 0 270 12

Hereinafter, an operation of the block interleaver 124 will be explainedin detail.

Specifically, as shown in FIG. 30 , the input bit v_(i)(0≤i<N_(C)×N_(r1)) is written in r_(i) row of c_(i) column of the firstpart of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor$and r_(i)=(i mod N_(r1)), respectively,

In addition, the input bit v_(i) (N_(C)×N_(r1)≤N_(ldpc)) is written inr_(i) row of c_(i) column of the second part of the block interleaver124. Herein, c_(i) and r_(i) satisfy

$c_{i} = \left\lfloor \frac{\left( {i - {N_{C} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor$and r_(i)=N_(r1) {(i−N_(C)×N_(r1)) mod N_(r2)}, respectively.

An output bit q_(j)(0≤j<N_(ldpc)) is read from c_(j) column of r_(j)row. Herein, r_(j) and c_(j) satisfy

$r_{j} = \left\lfloor \frac{j}{N_{c}} \right\rfloor$and c_(j)=(j mod N_(C)), respectively.

For example, when the length N_(ldpc) of an LDPC codeword is 64800 andthe modulation method is 256-QAM, the order of bits output from theblock interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈,q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . . ,v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, v₆₄₇₉₉). Herein, the indexes ofthe right side of the foregoing equation may be specifically expressedfor the eight (8) columns as 0, 7920, 15840, 23760, 31680, 39600, 47520,55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441, . . . , 7919,15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360, 63540, 63720,63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719, 63899, 64079,64259, 64439, 64619, 64799.

Hereinafter, the interleaving operation of the block interleaver 124will be explained in detail.

The block interleaver 124 may interleave by writing a plurality of bitgroups in each column in bit group wise in a column direction, andreading each row of the plurality of columns in which the plurality ofbit groups are written in bit group wise in a row direction.

In this case, the number of columns constituting the block interleaver124 may vary according to a modulation method, and the number of rowsmay be the length of the LDPC codeword/the number of columns.

For example, when the modulation method is 16-QAM, the block interleaver124 may be formed of 4 columns. In this case, when the length N_(ldpc)of the LDPC codeword is 16200, the number of rows is 4050 (=16200/4).

Hereinafter, the method for interleaving the plurality of bit groups inbit group wise by the block interleaver 124 will be explained in detail.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns, the block interleaver 124 mayinterleave by writing the bit groups as many as the number of bit groupsdivided by the number of columns in each column serially in bit groupwise.

For example, when the modulation method is 16-QAM and the lengthN_(ldpc) of the LDPC codeword is 16200, the block interleaver 124 may beformed of four (4) columns each including 4050 rows. In this case, sincethe LDPC codeword is divided into (16200/360=45) number of bit groupswhen the length N_(ldpc) of the LDPC codeword is 64800, the number ofbit groups (=45) of the LDPC codeword may not be an integer multiple ofthe number of columns (=4) when the modulation method is 16-QAM. Thatis, remainder is generated when the number of bit groups of the LDPCcodeword is divided by the number of columns.

As described above, when the number of the bit groups constituting theLDPC codeword is not an integer multiple of the number of columnsconstituting the block interleaver 124, the block interleaver 124 maydivide each column into N number of parts (N is an integer greater thanor equal to 2) and perform interleaving.

To be specific, the block interleaver 124 may divide each column into apart which includes rows as many as the number of bits included in a bitgroup which can be written in each column in bit group wise (that is,the first part) and a part including remaining rows (that is, the secondpart), and perform interleaving using each of the divided part.

Here, the part which includes rows as many as the number of bitsincluded in a bit group that can be written in bit group wise, that is,the first part may be composed of rows as many as an integer multiple ofM. That is, when the modulation method is 256-QAM, each column of theblock interleaver 124 consists of 4050 rows, and thus each column of theblock interleaver 124 may be composed of the first part including 3960(=360×11) rows and the second part including 90 (=4050−3960) rows.

In this case, the block interleaver 124, after sequentially writing atleast a part of bit groups which can be written in bit group wise toeach of the plurality of columns from among the plurality of bit groups,may divide and write remaining bit groups at an area remaining from anarea where at least a part of bit groups are written at each of aplurality of columns. That is, the block interleaver 124 may write bitsincluded in at least a part of bit groups that can be written in thefirst part of each column in bit group wise, and divide and write thebits included in the remaining bit group in the second part of eachcolumn.

For example, when the modulation method is 16-QAM, as illustrated inFIGS. 31 and 32 , the block interleaver 124 may include 4 columns andeach column can be divided into the first part including 3960 rows andthe second part including 90 rows.

In this case, the block interleaver 124 write bits included in the bitgroup that can be written in group wise in the first part of each columnin a column direction.

That is, the block interleaver 124, as illustrated in FIGS. 31 and 32 ,may write bits included in bit group (Y₀), (Y₁) . . . (Y₁₀) from the1^(st) row to the 3960^(th) row constituting the first part of the firstcolumn, write bits included in bit group (Y₁₁), (Y₁₂) . . . (Y₂₁) fromthe first row constituting the first part of the second column to the3960^(th) row, . . . , write bits included in each of bit group (Y₂₂₅),(Y₂₃). (Y₃₂) from the 1^(st) row to the 3960^(th) row constituting thefirst part of the 3^(rd) column, and write bits included in bit group(Y₃₃), (Y₃₄) . . . (Y₄₃) from the first row constituting the first partof the fourth column to the 3960^(th) row.

As described above, the block interleaver 124 writes bits included inthe bit group that can be written in group wise in the first part ofeach column in bit group wise.

Thereafter, the block interleaver 124 may divide bits included inremaining bit groups excluding the group written in the first part ofeach column, from among a plurality of groups, and write in the secondpart of each column in a column direction. In this case, the blockinterleaver 124, so that the same number of bits can be written in thesecond part of each column, may divide the bits included in theremaining bit groups excluding the bit group written in the first partof a column into the number of columns, and write the divided bit toeach column of the second part in a column direction.

For example, as illustrated in FIG. 31 , when the last group of the LDPCcodeword, that is, the bit group (Y₄₄) remains, the block interleaver124 may divide included in the group (Y₄₃) into four, and sequentiallywrite the divided bits to the second part of each column. Accordingly,the bits constituting the last group are not written in the same columnof the second part, but written in a plurality of columns.

That is, the block interleaver 124 may write bits from the 1^(st) row tothe 90^(th) row of the second part of the first column, may write bitsfrom the 1^(st) row to the 90^(th) row of the second part of the secondcolumn, may write bits from the 1^(st) row to the 90^(th) row of thesecond part of the third column, may write bits from the 1^(st) row tothe 90^(th) row of the second part of the fourth column. In this case,the block interleaver 124 may write bits in the second part of eachcolumn in a column direction as illustrated in FIG. 31 .

Meanwhile, in the aforementioned example, it is described that the blockinterleaver 124 write bits in the second part in a column direction, itis merely exemplary. That is, the block interleaver 124 may write bitsin a plurality of columns of the second part in a row direction.Meanwhile, the block interleaver 124 may write bits in the same manneras mentioned above, as to the first part.

To be specific, referring to FIG. 32 , the block interleaver 124 maywrite bits from the 1^(st) row of the second part of the first column tothe 1^(st) row of the second part of the fourth column, write bits fromthe 2^(nd) row of the second part of the first column to the 2^(nd) rowof the second part of the fourth column, . . . , and write bits from the90^(th) row of the second part of the first column to the 90^(th) row ofthe second part of the fourth column.

Meanwhile, the block interleaver 124 sequentially reads the bits writtenin each row of each part in a row direction. That is, the blockinterleaver 124, as illustrated in FIGS. 31 and 32 , may sequentiallyread the bits written in each row of the first part of a plurality ofcolumns in a row direction, and sequentially read the bits written ineach row of the second part of a plurality of columns in a rowdirection.

As described above, the block interleaver 124 may interleave theplurality of bit groups of the LDPC codeword in the method describedabove with reference to FIGS. 27 to 32 .

The modulator 130 maps the interleaved LDPC codeword onto a modulationsymbol. Specifically, the modulator 130 may demultiplex the interleavedLDPC codeword, modulate the demultiplexed LDPC codeword, and map theLDPC codeword onto a constellation.

First, the modulator 130 demultiplexes the interleaved LDPC codeword. Toachieve this, the modulator 130 may include a demultiplexer (not shown)to demultiplex the interleaved LDPC codeword.

The demultiplexer (not shown) demultiplexes the interleaved LDPCcodeword. Specifically, the demultiplexer (not shown) performsserial-to-parallel conversion with respect to the interleaved LDPCcodeword, and demultiplexes the interleaved LDPC codeword into a cellhaving a predetermined number of bits (or a data cell).

For example, as shown in FIG. 33 , the demultiplexer (not shown)receives the LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from theinterleaver 120, outputs the received LDPC codeword bits to a pluralityof substreams serially, converts the input LDPC codeword bits intocells, and outputs the cells.

In this case, the bits having the same index in each of the plurality ofsubstreams may constitute the same cell. Accordingly, the cells may beconfigured like (y_(0,0), y_(1,0), y_(η MOD−1,0))=(q₀, q₁, q_(η MOD−1)),(y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD), q_(η MOD+1), . . ., q_(2×η MOD−1)), . . . .

Herein, the number of substreams, N_(substreams), may be equal to thenumber of bits constituting a modulation symbol, η_(MOD). Accordingly,the number of bits constituting each cell may be equal to the number ofbits constituting a modulation symbol (that is, a modulation order).

For example, when the modulation method is 16-QAM, the number of bitsconstituting the modulation symbol, η_(MOD), is 8 and thus the number ofsubstreams, N_(substreams), is 4, and the cells may be configured like(y_(0,0), y_(1,0), y_(2,0), y_(3,0))=(q₀, q₁, q₂, q₃, q₄), (y_(0,1),y_(1,1), y_(2,1), y_(3,1,1))(q₄, q₅, q₆, q₇), (y_(0,2), y_(1,2),y_(2,2), y_(3,2))(q₈, q₉, q₁₀, q₁₁), . . . .

The modulator 130 may map the demultiplexed LDPC codeword ontomodulation symbols.

Specifically, the modulator 130 may modulate bits (that is, cells)output from the demultiplexer (not shown) in various modulation methodssuch as 16-QAM, etc. For example, when the modulation method is QPSK,16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM, the number of bitsconstituting the modulation symbol, η_(MOD) (that is, the modulationorder), may be 2, 4, 6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer (not shown)is formed of as many bits as the number of bits constituting themodulation symbol, the modulator 130 may generate the modulation symbolby mapping each cell output from the demultiplexer (not shown) onto aconstellation point serially. Herein, the modulation symbol correspondsto a constellation point on the constellation.

However, the above-described demultiplexer (not shown) may be omittedaccording to circumstances. In this case, the modulator 130 may generatemodulation symbols by grouping a predetermined number of bits frominterleaved bits serially and mapping the predetermined number of bitsonto constellation points. In this case, the modulator 130 may generatethe modulation symbols by mapping η_(MOD) number of bits onto theconstellation points serially according to a modulation method.

The modulator 130 may modulate by mapping cells output from thedemultiplexer (not shown) onto constellation points in a non-uniformconstellation (NUC) method.

In the non-uniform constellation method, once a constellation point ofthe first quadrant is defined, constellation points in the other threequadrants may be determined as follows. For example, when a set ofconstellation points defined for the first quadrant is X, the setbecomes −conj(X) in the case of the second quadrant, becomes conj(X) inthe case of the third quadrant, and becomes −(X) in the case of thefourth quadrant.

That is, once the first quadrant is defined, the other quadrants may beexpressed as follows:

-   -   1 Quarter (first quadrant)=X    -   2 Quarter (second quadrant)=−conj(X)    -   3 Quarter (third quadrant)=conj(X)    -   4 Quarter (fourth quadrant)=−X

Specifically, when the non-uniform M-QAM is used, M number ofconstellation points may be defined as z={z₀, z₁, . . . , z_(M−1)}. Inthis case, when the constellation points existing in the first quadrantare defined as {x₀, x₁, x₂, . . . , x_(M/4−1)}, z may be defined asfollows:

-   -   from z₀ to z_(M/4−1)=from x₀ to x_(M/4)    -   from z_(M/4) to z_(2×M/4−1)=−conj(from x₀ to x_(M/4))    -   from z_(2×M/4) to z_(3×M/4−1)=conj(from x₀ to x_(M/4))    -   from z_(3×M/4) to z_(4×M/4−1)=−(from x₀ to x_(M/4))

Accordingly, the modulator 130 may map the bits [y₀, . . . , y_(m−1)]output from the demultiplexer (not shown) onto constellation points inthe non-uniform constellation method by mapping the output bits ontoz_(L) having an index of

$L = {\sum\limits_{i = 0}^{m - 1}{\left( {y_{1} \times 2^{m - 1}} \right).}}$An example of the constellation defined according to the non-uniformconstellation method may be expressed as in table 31 presented belowwhen the code rate is 5/15, 7/15, 9/15, 11/15, 13/15:

TABLE 31 x/shape 5/15 7/15 9/15 11/15 13/15 x₀   0.3192 + 0.5011i  0.2592 + 0.4888i   0.2386 + 0.5296i   0.9342 + 0.9847i   0.9517 +0.9511i x₁   0.5011 + 0.3192i   0.4883 + 0.2502i   0.5296 + 0.2386i  0.9866 + 0.2903i   0.9524 + 0.3061i x₂   0.5575 + 1.1559i   0.5072 +1.1980i   0.4882 + 1.1934i   0.2716 + 0.9325i   0.3067 + 0.9524i x₃  1.1559 + 0.5575i   1.1980 + 0.5072i   1.1934 + 0.4882i   0.2901 +0.2695i   0.3061 + 0.3067i x₄ −0.3195 + 0.5011i −0.2592 + 0.4888i−0.2686 + 0.5296i −0.9342 + 0.9847i −0.9517 + 0.9511i x₅ −0.5011 +0.3192i −0.4888 + 0.2592i −0.5296 + 0.2386i −0.9866 + 0.2903i −0.9524 +0.3061i x₆ −0.5575 + 1.1559i −0.5072 + 1.1980i −0.4882 + 1.1934i−0.2716 + 0.9325i −0.3067 + 0.9524i x₇ −1.1550 + 0.5575i −1.1980 +0.5072i −1.1934 + 0.4882i −0.2901 + 0.2695i −0.3061 + 0.3067i x₈  0.3192 − 0.5011i   0.2592 − 0.4888i   0.2386 − 0.5296i   0.9342 −0.9847i   0.9517 − 0.9511i x₉   0.9911 − 0.3102i   0.4888 − 0.2592i  0.5296 − 0.2386i   0.9866 − 0.2903i   0.9524 − 0.3061i x₁₀   0.5575 −1.1559i   0.5072 − 1.1980i   0.4882 − 1.1934i   0.2716 − 0.9325i  0.3067 − 0.9524i x₁₁   1.1559 − 0.5575i   1.1980 − 0.5072i   1.1934 −0.4882i   0.2901 − 0.2695i   0.3061 − 0.3067i x₁₂ −0.3192 − 0.5011i−0.2592 − 0.4888i −0.2386 − 0.5296i −3.9342 − 0.9847i −0.9517 − 0.9511ix₁₃ −0.5011 − 0.3192i −0.4888 − 0.2592i −0.5296 − 0.2386i −0.9866 −0.2903i −0.9524 − 0.3061i x₁₄ −0.5575 − 1.1559i −0.5072 − 1.1980i−0.4882 − 1.1934i −0.2716 − 0.9325i −0.3057 − 0.9524i x₁₅   1.1559 −0.5575i −1.1980 − 0.5072i −1.1934 − 0.4882i   0.2901 − 0.7695i −0.3061 −0.3067i

The interleaving is performed in the above-described method for thefollowing reasons.

Specifically, when the LDPC codeword bits are mapped onto the modulationsymbol, the bits may have different reliability (that is, receivingperformance or receiving probability) according to where the bits aremapped onto in the modulation symbol. The LDPC codeword bits may havedifferent codeword characteristics according to the configuration of aparity check matrix. That is, the LDPC codeword bits may have differentcodeword characteristics according to the number of 1 existing in thecolumn of the parity check matrix, that is, the column degree.

Accordingly, the interleaver 120 may interleave to map the LDPC codewordbits having a specific codeword characteristic onto specific bits in themodulation symbol by considering both the codeword characteristics ofthe LDPC codeword bits and the reliability of the bits constituting themodulation symbol.

For example, when the LDPC codeword formed of bit groups X₀ to X₄₄ isgroup-interleaved based on Equation 12 and Table 15, the groupinterleaver 122 may output the bit groups in the order of X₃, X₃₃, X₃₉,. . . , X₃₅, X₂₇.

In this case, the number of columns of the block interleaver 124 is four(4) and the number of rows in the first part is 3960 and the number ofrows in the second part is 90.

Accordingly, from among the 45 groups constituting the LDPC codeword 11bit groups (X₃, X₃₃, X₃₉, X₂, X₃₈, X₂₉, X₀, X₁₀, X₂₅, X₁₇, X₇) may beinputted to the first part of the first column of the block interleaver124, 11 bit groups (X₂₁, X₄₄, X₃₇, X₈, X₃₄, X₂₀, X₁, X₄, X₃₁, X₁₁, X₄₂)may be inputted to the first part of the second column of the blockinterleaver 124, 11 bit groups (X₂₂, X₁₃, X₁₂, X₂₈, X₂₆, X₄₃, X₃₀, X₁₄,X₁₆, X₂₃, X₂₄) may be inputted to the first part of the third column ofthe block interleaver 124, 11 bit groups (X₁₅, X₅, X₁₈, X₉, X₃₆, X₆,X₁₉, X₃₂, X₄₀, X₄₁, X₃₅) may be inputted to the first part of the fourthcolumn of the block interleaver 124.

The group X₂₇ is input to the second part of the block interleaver 124.To be specific, from among 360 bits constituting the group X₂₇, bits areserially inputted to the second part of the first column, the secondpart of the second column, the second part of the third column, and thesecond part of the fourth column by 90 bits.

In addition, the block interleaver 124 may output the bits inputted tothe 1^(st) row to the last row of each column serially, and the bitsoutputted from the block interleaver 124 may be inputted to themodulator 130 serially. In this case, the demultiplexer (not shown) maybe omitted or the bits may be outputted serially without changing theorder of bits inputted to the demultiplexer (not shown). Accordingly,the bits included in each of the bit groups X₃, X₂₁, X₂₂, X₁₅ mayconstitute the modulation symbol.

As described above, since a specific bit is mapped onto a specific bitin a modulation symbol through interleaving, a receiver side can achievehigh receiving performance and high decoding performance.

Hereinafter, a method for determining π(j), which is a parameter usedfor group interleaving, according to various exemplary embodiments, willbe explained. The criteria which needs to be considered is as shownbelow:

Criteria 1) Determine different interleaving orders based on amodulation method and a code rate.

Criteria 2) Consider functional features of each bit group of an LDPCcodeword and functional features of bits constituting a modulationsymbol at the same time.

For example, in an LDPC codeword, performance characteristics vary ingroup wise by the degree of variable node corresponding to bitsconstituting of each group, that is, the number of edges connected tothe variable node, and characteristics of graphs connected to thevariable node. In general, the greater is the degree of the variablenode, the better is the performance.

Meanwhile, bits constituting a modulation symbol may have differentperformance characteristics. For example, when using non-uniform 16-QAM(hereinafter, 16-NUQ) constellation as illustrated in Table 31, withrespect to four (4) bits y₀, y₁, y₂, y₃ constituting a 16-NUQ symbol,signal reception performance of each bit (P(yi)) is represented byP(y₀)≥P(y₁)≥P(y₂)≥P(y₃).

Therefore, when using an LDPC code of which a length is 16200, and16-NUQ, the characteristics of the LDPC code and a modulation methodneed to be considered, and to which bit, from among four (4) bitsconstituting a 16-NUQ symbol, each bit group of 45 bit groups is mappedneeds to be selected.

In this case, the first column of the block interleaver 124 correspondsto y₀ having the highest performance from among four (4) bitsconstituting the 16-NUQ symbol, the second column corresponds to y₁, thethird column corresponds to y₂, 4^(th) column corresponds to y₃. Here,45 is not a multiple number of four (4), and thus, one (1) bit groupscorresponding to the second part of the block interleaver 124 maycorrespond four (4) bits constituting a 16-NUQ symbol. For example, whenone bit group of an LDPC codeword is written in the first column and the4^(th) column of the second part, and this bit group may be mapped ony₀, y₁, y₂, y₃.

Accordingly, when an LDPC codeword of which a length is 16200 and 16-NUQare used, from among four (4) bits constituting a 16-NUQ symbol, eleven(11) bit groups to be mapped onto y₀ need to be selected, eleven (11)bit groups to be mapped onto y₁ need to be selected, eleven (11) bitgroups to be mapped onto y₂ need to be selected, eleven (11) bit groupsto be mapped onto y₃ need to be selected, and one (1) bit group to bemapped onto y₀, y₁, y₂, y₃ needs to be selected.

Meanwhile, in order to predict decoding performance in reference to anLDPC code and a modulation method, a density evolution method can beused. The density evolution method is performed by receiving aprobability density function (PDF) with respect to a log-likelihoodratio (LLR) for each bit group of an LDPC codeword and calculating aminimum signal-to-noise ratio (SNR) which satisfies quasi error free(QEF). Here, the SNR is called a noise threshold.

The 16-NUQ is formed of four (4) bit levels. Here, a PDF of an LLR valuewhich corresponds to each bit level is g₀(x), g₁(x), g₂(x), g₃(x). Thatis, when i is an integer between 0 and 3, from among four (4) bitsconstituting a 16-NUQ symbol, the PDF with respect to the LLR value ofthe channel output value corresponding to y₁ is g₁(x).

Meanwhile, from among 45 bit groups constituting an LDPC codeword ofwhich a length is 16200, the PDF of a channel LLR with respect to eleven(11) bit groups corresponding to the first part is f₁(x), the PDF of thechannel LLR with respect to eleven (11) bit groups corresponding to thesecond part is f₂(x), the PDF of the channel LLR with respect to eleven(11) bit groups corresponding to the third part is f₃(x), the PDF of thechannel LLR with respect to eleven (11) bit groups corresponding to thefourth part is f₁(x). In addition, the PDF of the channel LLR withrespect to one (1) bit group corresponding to the first columns, secondcolumns, third columns and 4^(th) columns of the second part is f₅(x).In this case, the relation formula as Equation 22 shown below can beconceived.f ₁(x)=g ₀(x),f ₂(x)=g ₁(x),f ₃(x)=g ₂(x),f ₄(x)=g ₃(x),f ₅(x)=(g ₀(x)+g ₁(x)+g ₂(x)+g ₃(x))/4  [Equation 22]

In various exemplary embodiments, in a process of designing a groupinterleaver by determining π(j) which is a parameter used for groupinterleaving, the first step is a process to select one from among f₁(x)to f₅(x) as each of PDFs of LLR values of 45 bit groups constituting anLDPC codeword of which length is 16200.

At step 1-1 of the first step of a group interleaver design, PDFs of LLRvalues of all bit groups are not selected. Therefore, when using thedensity evolution method, the PDFs with respect to the LLR values of theall bit groups use f_(remain)(x) value according to Equation 23. This isa weighted average of PDFs which are not yet selected.f _(remain)(x)=(11×f ₁(x)+11×f ₂ (x)+11×f ₃(x)+11×f ₄(x)+f₅(x))/45  [Equation 23]

At step 1-2 of the first step of the group interleaver design, a PDF ofan LLR value of each bit group is selected from among f₁(x) to f₅(x).There are a total of 45 bit groups, and a total of five (5) PDFs can beselected for respective of bit groups. For example, it can be assumedthat f₁(x) is selected as a PDF of the first bit group, and PDFs of theremaining bit groups are not selected. In this case, for PDFs of theremaining bit groups, f_(remain)(x) is used as Equation 24 shown below.This is a weighted average value of PDFs which are not yet selected.f _(remain)(x)=(10×f ₁(x)+11×f ₂ (x)+11×f ₃(x)+11×f ₄(x)+f₅(x))/44  [Equation 24]

At the above step, in order for f₁(x) to be selected as the PDF of thefirst bit group, one of cases in which an value of a noise thresholdobtained by the density evolution method is the least may be selectedarbitrarily, according to an exemplary embodiment. The noise thresholdsare different according to channels, and the channel and noise thresholdconsidered in the present invention will be described in greater detaillater

At step 1-3 of the group interleaver design, a next bit group for whicha PDF is selected, and also, the PDF is selected for this bit group,based on the step 1-2. For example, if it is assumed that, at the 1-2step, f₁(x) is selected as the PDF of the first bit group since theaverage value of the noise threshold is the least in this case, f₃(x) isselected as a PDF of the second bit group. In this case, PDFs of theremaining bit groups uses f_(remain)(x) as Equation 25 shown below. Thisis a weighted average PDFs which are not yet selected.f _(remain)(x)=(10×f ₁(x)+11×f ₂ (x)+10×f ₃(x)+11×f ₄(x)+f₅(x))/43  [Equation 25]

After performing through step 1-46 of the first step of the groupinterleaver design in the same manner as above, one PDF from among f₁(x)to f₅(x) is selected or allocated to each of 45 bit groups. That is,when the first step of the group interleaver design is completed, PDFsof LLR values of the respective of 45 bit groups are selected from f₁(x)to f₅(x).

In the above process, after noise threshold is calculated by using thedensity evolution, and based on the calculated noise threshold, aposition where each bit group corresponds to each column of the firstpart of the block interleaver 124 by each step is determined. The noisethreshold is defined as different values according to a given channelenvironment, and thus, a channel environment considered in the systemneeds to be reflected for determination. In other words, a performanceof a code by interleaving is substantially changeable according to achannel which evaluates a performance, and therefore, a channel shouldbe considered for the interleaving pattern.

For example, in general, in many cases, a good interleaving pattern inAWGN channel is not good in a Rayleigh channel. In this case, if achannel environment where a given system is used is closer to theRayleigh channel, it may be better to select the interleaving patternwhich is good in Rayleigh than the interleaving pattern which is good inthe AWGN channel.

In conclusion, in order to determine the interleaving pattern, not onlya predetermined channel environment but also various channelenvironments to be considered in the system should be considered tocalculate a good interleaving pattern.

It is considered that there are channels C₁, C₂, . . . , C_(k) to beconsidered in the present invention, a noise threshold which is used forfinal determination is as shown below, after each noise thresholdcalculated in the 1-i step is calculated, and the noise thresholdthereof is indicated as TH₁[i], TH₂[i], . . . , TH_(k)[i].TH[i]=W ₁ *TH ₁ [i]+W ₂ *TH ₂ [i]+ . . . +W _(k) *TH _(k) [i],

Here, W₁+W₂+ . . . +W_(k)=1, W₁, W₂, . . . , W_(k)>0.

W₁, W₂, . . . , W_(k) are adjusted according to a level of importance ofa channel, that is, W₁, W₂, . . . , W_(k) are is adjusted to be large inan important channel, and W₁, W₂, . . . , W_(k) are adjusted to be smallin a less important channel (ex: when considering two different channelssuch as AWGN and Rayleigh, if it seems that the level of importance ofany channel is deemed higher, asymmetric value such as W₁=0.25, W₂=0.75is set regarding weight values W₁, W₂ which correspond to each channel).

The second step of the group interleaver design is to generate aplurality of π(j)s which satisfy the conditions determined at the firststep, observe actual bit error rate (BER) and frame error rate (FER)performances for a predetermined SNR value, and select π(j) having thebest performance. As such, the reason why the step of measuring actualperformances is used in addition to the density evolution is that thedensity evolution may not estimate a correct performance of the LDPCcode which has a limited length because the density evolution calculatesa theoretical noise threshold under an assumption that a length of theLDPC codeword is unlimited.

In general, π(j) which satisfies a predetermined condition in the firststep is generated by 50, and then in each channel, a performance istested regarding FER=10{circumflex over ( )}−3 area. Out of this, 5interleaver patterns of which SNR gain is estimated to be largest in thetarget FER (ex: FER=10{circumflex over ( )}−6) are selected, performanceof the final target FER is tested, and then the interleaver having thebest performance is finally selected. Here, a method of selecting theinterleaver of which SNR gain seems the largest is that, FERperformance, which is required by the system from the actualcomputational experiment result with respect to FER=10{circumflex over( )}−3 area, is estimated through extrapolation, and then estimatedperformance in the target FER which is requested in the system iscompared, and the interleaver having a better performance is determinedas an excellent interleaver. In the present invention, a method ofextrapolation is applied based on a linear function for convenientexplanation, but various extrapolation methods may be applied.

Meanwhile, FIG. 34 is a view to illustrate an example of performanceextrapolation estimated from computational experimental result.

However, if the finally selected interleaver shows the error-floor onthe target FER, π(j) which satisfies a predetermined condition in firststep is further generated by 50 and the above process is repeated.

According to the above-described method, π(j) of Tables 15-27 used forgroup interleaving can be determined.

Hereinbelow, step 2 of the group interleaver design will be described ingreater detail.

Meanwhile, as described above, in that each of bit groups constitutingthe LDPC codeword correspond to each column group of the parity checkmatrix, a degree of each column group has an effect on decodingperformance of the LDPC codeword.

For example, that a degree of column groups is relatively high indicatesthat there are relatively larger number of parity check equations whichare related to bit groups corresponding to column groups, the bit groupswhich correspond to column groups having a relatively high degree withina parity check matrix formed of a plurality of column groups may have agreater effect on decoding performance of the LDPC codeword rather thanbit groups which correspond to column groups having a relatively lowdegree. In other words, if column groups having a relatively high degreeare not mapped appropriately, the performance of the LDPC codeword willbe substantially degraded.

Therefore, the group interleaver may be designed such that a bitgroup(s) having the highest degree, from among the bit groupsconstituting the LDPC codeword, is interleaved according to the π(j) andmapped to a specific bit of the modulation symbol (or transmissionsymbol), and the other bit groups not having the highest degree israndomly mapped to the modulation symbol. Under this condition, byobserving actual BER/FER performance, the case where the performance ofthe LDPC codeword is substantially degraded may be avoided.

Hereinbelow, a case where the encoder 110 performs LDPC encoding byusing the code rate 5/15 to generate an LDPC codeword having the lengthof 16200, and constitutes a modulation symbol by using 16-NUQ will bedescribed in a greater detail.

In this case, the encoder 110 may perform LDPC encoding based on theparity check matrix comprising the information word submatrix defined byTable 14 and the parity submatrix having a diagonal configuration.

Accordingly, the parity check matrix is formed of 45 column groups, andfrom among the 45 column groups, 10 column groups have the degree of 10,7 column groups have the degree of 9, 28 column groups have the degreeof 1.

Therefore, with respect to only 10 column groups of which the degree is10, from among the 45 column groups, several π(j) for the 10 columngroups may be generated to satisfy a predetermined condition in thefirst step of the group interleaver design, and π(j) for the othercolumn groups may be remain as a blank. The bit groups which correspondto the other column groups may be set to be mapped randomly onto bitsconstituting a modulation symbol. Then, π(j) for 10 column groups havingthe most excellent performance is selected by observing actual BER/FERperformance regarding a specific SNR value. By fixing a part of π(j),i.e. π(j) for 10 column groups selected as described above, substantialdegradation of the performance of the LDPC codeword may be avoided.

TABLE 32 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 2021 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4041 42 43 44 interleaver output π(j)-th block 10  7  8 11 of Group- wise13 12 14  5  9  6 interleaver input

On the other hand, Table 32 may be presented as below Table 32-1

TABLE 32-1 Order of group to be block interleaved π(j) (0 ≤ j < 45) j-thblock of  7 10 14 20 23 24 29 34 36 38 Group-wise interleaver outputπ(j)-th block 10  7  8 11 13 12 14  5  9  6 of Group- wise interleaverinput

In case of Table 32, Equation 21 may be expressed as Y₇=X_(π(7))=X₁₀,Y₁₀=X_(π(10))=X₇, Y₁₄=X_(π(14))=X₈, Y₂₀=X_(π(20))=X₁₁,Y₂₃=X_(π(23))=X₁₃, Y₂₄=X_(π(24))=X₁₂, Y₂₉=X_(π(29))=X₁₄,Y₃₄=X_(π(34))=X₅, Y₃₆=X_(π(36))=X₉, Y₃₈=X_(π(38))=X₆.

That is, the group interleaver 122 may rearrange the order of theplurality of bit groups by changing the 10^(th) bit group to the 7^(th)bit group, the 7^(th) bit group to the 10^(th) bit group, the 8^(th) bitgroup to the 14^(th) bit group, the 11^(th) bit group to the 20^(th) bitgroup, the 13^(th) bit group to the 23^(rd) bit group, the 12^(th) bitgroup to the 24^(th) bit group, the 14^(th) bit group to the 29^(th) bitgroup, the 5^(th) bit group to the 24^(th) bit group, the 9^(th) bitgroup to the 36^(th) bit group, and the 6^(th) bit group to the 38^(th)bit group, and by rearranging randomly the other bit groups.

In a case where some bit groups are already fixed, the aforementionedfeature is applied in the same manner. In other words, bit groups whichcorrespond to column groups having a relatively high degree from amongthe other bit groups which are not fixed may have a greater effect ondecoding performance of the LDPC codeword than bit groups whichcorrespond to column groups having a relatively low degree. That is,even in the case where degradation of the performance of the LDPCcodeword is prevented by fixing the bit groups having the highestdegree, the performance of the LDPC codeword may vary according to amethod of mapping the other bit groups. Accordingly, a method of mappingbit groups having the next highest degree needs to be selectedappropriately, to avoid the case where the performance is relativelypoor.

Therefore, in a case where bit groups having the highest degree arealready fixed, bit groups having the next highest degree, from among thebit groups constituting the LDPC codeword, may be interleaved accordingto the π(j) and mapped to a specific bit of a modulation symbol, and theother bit groups may be randomly mapped. Under this condition, byobserving actual BER/FER performance, the case where the performance ofthe LDPC codeword is substantially degraded may be avoided.

Hereinbelow, a case where the encoder 110 performs LDPC encoding byusing the code rate 5/15 to generate an LDPC codeword having the lengthof 16200, and constitutes a modulation symbol by using 16-NUQ will bedescribed in a greater detail.

In this case, the encoder 110 may perform LDPC encoding based on theparity check matrix comprising the information word submatrix defined byTable 14 and the parity submatrix having a diagonal configuration.

Accordingly, the parity check matrix is formed of 45 column groups, andfrom among the 45 column groups, 10 column groups have the degree of 10,7 column groups have the degree of 9, 28 column groups have the degreeof 1.

Therefore, in a case where 10 column groups of which the degree is 10are already fixed as in Table 32, so that, with respect to only 7 columngroups of which the degree is 9, from among the other 35 column groups,several π(j) for the 7 column groups may be generated to satisfy apredetermined condition in a first step of the group interleaver design,and π(j) for the other column groups may be remained as a blank. The bitgroups which correspond to the other column groups may be set to bemapped randomly onto bits constituting a modulation symbol. Then, π(j)for 7 column groups having the most excellent performance is selected byobserving actual BER/FER performance regarding a specific SNR value. Byfixing a part of π(j), i.e. π(j) for 7 column groups selected asdescribed above, substantial degradation of the performance of the LDPCcodeword may be avoided.

TABLE 33 Order of group to be block interleaved π(j)(0 ≤ j < 45) j-thblock of  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 2021 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4041 42 43 44 interleaver output π(j)-th block 10  7  8 11 of Group- 13 1214  5  9  6 wise interleaver input

On the other hand, Table 33 may be presented as below Table 33-1

TABLE 33-1 Order of group to be block interleaved π(j)(0 ≤j < 45) j-thblock of 0 3 6  7 10 14 17 18 20 23 24 29 30 33 34 36 38 Group-wiseinterleaver output π(j)-th block 3 2 0 10  7  8  1  4 11 13 12 14 16 15 5  9  6 of Group- wise interleaver input

In case of Table 33, Equation 21 may be expressed as Y₀=X_(π(0))=X₃,Y₃=X_(π(3))=X₂, Y₆=X_(π(6))=X₀, . . . , Y₃₄=X_(π(34))=X₅,Y₃₆=X_(π(36))=X₉, Y₃₈=X_(π(38))=X₆.

That is, the group interleaver 122 may rearrange the order of theplurality of bit groups by changing the 3^(rd) bit group to the 0^(th)bit group, the 2^(nd) bit group to the 3^(rd) bit group, the 0^(th) bitgroup to the 6^(th) bit group, . . . , the 5^(th) bit group to the34^(th) bit group, the 9^(th) bit group to the 36^(th) Jo bit group, andthe 6^(th) bit group to the 38^(th) bit group, and by rearrangingrandomly the other bit groups.

In the exemplary embodiments described above, the case of performingLDPC encoding based on the coding rate of 5/15 and the parity checkmatrix formed of the information word submatrix defined by Table 14 andthe parity submatrix having a diagonal configuration is described, butthis is merely exemplary, and even in a case of performing LDPC encodingbased on different code rates and different parity check matrix, π(j)can be determined based on the aforementioned method

The transmitting apparatus 100 may transmit the signal mapped onto theconstellation to a receiving apparatus (for example, 1200 of FIG. 35 ).For example, the transmitting apparatus 100 may map the signal mappedonto the constellation onto an Orthogonal Frequency DivisionMultiplexing (OFDM) frame using OFDM, and may transmit the signal to thereceiving apparatus 1200 through an allocated channel.

FIG. 35 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment. Referring to FIG. 35 ,the receiving apparatus 1200 includes a demodulator 1210, a multiplexer1220, a deinterleaver 1230 and a decoder 1240.

The demodulator 1210 receives and demodulates a signal transmitted fromthe transmitting apparatus 100. Specifically, the demodulator 1210generates a value corresponding to an LDPC codeword by demodulating thereceived signal, and outputs the value to the multiplexer 1220. In thiscase, the demodulator 1210 may use a demodulation method correspondingto a modulation method used in the transmitting apparatus 100. To do so,the transmitting apparatus 100 may transmit information regarding themodulation method to the receiving apparatus 2700, or the transmittingapparatus 100 may perform modulation using a pre-defined modulationmethod between the transmitting apparatus 100 and the receivingapparatus 1500.

The value corresponding to the LDPC codeword may be expressed as achannel value for the received signal. There are various methods fordetermining the channel value, and for example, a method for determininga Log Likelihood Ratio (LLR) value may be the method for determining thechannel value.

The LLR value is a log value for a ratio of the probability that a bittransmitted from the transmitting apparatus 100 is 0 and the probabilitythat the bit is 1. In addition, the LLR value may be a bit value whichis determined by a hard decision, or may be a representative value whichis determined according to a section to which the probability that thebit transmitted from the transmitting apparatus 100 is 0 or 1 belongs.

The multiplexer 1220 multiplexes the output value of the demodulator1210 and outputs the value to the deinterleaver 1230.

Specifically, the multiplexer 1220 is an element corresponding to ademultiplexer (not shown) provided in the transmitting apparatus 100,and performs an operation corresponding to the demultiplexer (notshown). That is, the multiplexer 1220 performs an inverse operation ofthe operation of the demultiplexer (not shown), and performs cell-to-bitconversion with respect to the output value of the demodulator 1210 andoutputs the LLR value in the unit of bit. However, when thedemultiplexer (not shown) is omitted from the transmitting apparatus100, the multiplexer 1220 may be omitted from the receiving apparatus1200.

The information regarding whether the demultiplexing operation isperformed or not may be provided by the transmitting apparatus 100, ormay be pre-defined between the transmitting apparatus 100 and thereceiving apparatus 1500.

The deinterleaver 1230 deinterleaves the output value of the multiplexer1220 and outputs the values to the decoder 1240.

Specifically, the deinterleaver 1230 is an element corresponding to theinterleaver 120 of the transmitting apparatus 100 and performs anoperation corresponding to the interleaver 120. That is, thedeinterleaver 1230 deinterleaves the LLR value by performing theinterleaving operation of the interleaver 120 inversely.

To do so, the deinterleaver 1230 may include a block deinterleaver 1231,a group twist deinterleaver 1232, a group deinterleaver 1233, and aparity deinterleaver 1234 as shown in FIG. 36 .

The block deinterleaver 1231 deinterleaves the output of the multiplexer1220 and outputs the value to the group twist deinterleaver 1232.

Specifically, the block deinterleaver 1231 is an element correspondingto the block interleaver 124 provided in the transmitting apparatus 100and performs the interleaving operation of the block interleaver 124inversely.

That is, the block deinterleaver 1231 deinterleaves by writing the LLRvalue output from the multiplexer 1220 in each row in the row directionand reading each column of the plurality of rows in which the LLR valueis written in the column direction by using at least one row formed ofthe plurality of columns.

In this case, when the block interleaver 124 interleaves by dividing thecolumn into two parts, the block deinterleaver 1231 may deinterleave bydividing the row into two parts.

In addition, when the block interleaver 124 writes and reads in and fromthe bit group that does not belong to the first part in the rowdirection, the block deinterleaver 1231 may deinterleave by writing andreading values corresponding to the group that does not belong to thefirst part in the row direction.

Hereinafter, the block deinterleaver 1531 will be explained withreference to FIG. 37 . However, this is merely an example and the blockdeinterleaver 1531 may be implemented in other methods.

An input LLR v_(i) (0≤i<N_(ldpc)) is written in a r_(i) row and a c_(i)column of the block deinterleaver 1531. Herein, c_(i)=(i mod N_(c)

$r_{i} = {\left\lfloor \frac{i}{N_{c}} \right\rfloor.}$) and

On the other hand, an output LLR q_(i)(0≤i<N_(c)×N_(r1)) is read from ac_(i) column and a r_(i) row of the first part of the blockdeinterleaver 1531. Herein,

${c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor},$r_(i)=(i mod N_(r1)).

In addition, an output LLR q_(i)(N_(c)×N_(r1)≤i<N_(ldpc)) is read from ac_(i) column and a r_(i) row of the second part. Herein,

${c_{i} = \left\lfloor \frac{\left( {i - {N_{c} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor},$r_(i)=N_(r1)+{(i−N_(c)×N_(r1)) mode N_(r2)}.

The group twist deinterleaver 1232 deinterleaves the output value of theblock deinterleaver 1231 and outputs the value to the groupdeinterleaver 1233.

Specifically, the group twist deinterleaver 1232 is an elementcorresponding to the group twist interleaver 123 provided in thetransmitting apparatus 100, and may perform the interleaving operationof the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 1232 may rearrange the LLR valuesof the same bit group by changing the order of the LLR values existingin the same bit group. When the group twist operation is not performedin the transmitting apparatus 100, the group twist deinterleaver 1232may be omitted.

The group deinterleaver 1233 (or the group-wise deinterleaver)deinterleaves the output value of the group twist deinterleaver 1232 andoutputs the value to the parity deinterleaver 1234.

Specifically, the group deinterleaver 1233 is an element correspondingto the group interleaver 122 provided in the transmitting apparatus 100and may perform the interleaving operation of the group interleaver 122inversely.

That is, the group deinterleaver 1233 may rearrange the order of theplurality of bit groups in bit group wise. In this case, the groupdeinterleaver 1233 may rearrange the order of the plurality of bitgroups in bit group wise by applying the interleaving method of Tables15 to 27 inversely according to a length of the LDPC codeword, amodulation method and a code rate.

The parity deinterleaver 1234 performs parity deinterleaving withrespect to the output value of the group deinterleaver 1233 and outputsthe value to the decoder 1240.

Specifically, the parity deinterleaver 1234 is an element correspondingto the parity interleaver 121 provided in the transmitting apparatus 100and may perform the interleaving operation of the parity interleaver 121inversely. That is, the parity deinterleaver 1234 may deinterleave theLLR values corresponding to the parity bits from among the LLR valuesoutput from the group deinterleaver 1233. In this case, the paritydeinterleaver 1234 may deinterleave the LLR value corresponding to theparity bits inversely to the parity interleaving method of Equation 18.

However, the parity deinterleaver 1234 may be omitted depending on thedecoding method and embodiment of the decoder 1240.

Although the deinterleaver 1230 of FIG. 35 includes three (3) or four(4) elements as shown in FIG. 36 , operations of the elements may beperformed by a single element. For example, when bits each of whichbelongs to each of bit groups X_(a), X_(b), X_(c), X_(d) constitute asingle modulation symbol, the deinterleaver 1230 may deinterleave thesebits to locations corresponding to their bit groups based on thereceived single modulation symbol.

For example, when the code rate is 5/15 and the modulation method is16-QAM, the group deinterleaver 1233 may perform deinterleaving based ontable 15.

In this case, bits each of which belongs to each of bit groups X₃, X₂₁,X₂₂, X₁₅ may constitute a single modulation symbol. Since one bit ineach of the bit groups X₃, X₂₁, X₂₂, X₁₅ constitutes a single modulationsymbol, the deinterleaver 1230 may map bits onto decoding initial valuescorresponding to the bit groups X₃, X₂₁, X₂₂, X₁₅ based on the receivedsingle modulation symbol.

The decoder 1240 may perform LDPC decoding by using the output value ofthe deinterleaver 1230. To achieve this, the decoder 1240 may include anLDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 1240 is an element corresponding to theencoder 110 of the transmitting apparatus 100 and may correct an errorby performing the LDPC decoding by using the LLR value output from thedeinterleaver 1230.

For example, the decoder 1240 may perform the LDPC decoding in aniterative decoding method based on a sum-product algorithm. Thesum-product algorithm is one example of a message passing algorithm, andthe message passing algorithm refers to an algorithm which exchangesmessages (e.g., LLR value) through an edge on a bipartite graph,calculates an output message from messages input to variable nodes orcheck nodes, and updates.

The decoder 1240 may use a parity check matrix when performing the LDPCdecoding. In this case, the parity check matrix used in the decoding mayhave the same configuration as that of the parity check matrix used inthe encoding of the encoder 110, and this has been described above withreference to FIGS. 20 to 22 .

In addition, information on the parity check matrix and information onthe code rate, etc. which are used in the LDPC decoding may bepre-stored in the receiving apparatus 1200 or may be provided by thetransmitting apparatus 100.

FIG. 38 is a flowchart to illustrate an interleaving method of atransmitting apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by LDPC encoding based on a paritycheck matrix (S1410), and the LDPC codeword is interleaved (S1420).

Then, the interleaved LDPC codeword is mapped onto a modulation symbol(S1430). In this case, a bit included in a predetermined bit group fromamong a plurality of bit groups constituting the LDPC codeword may bemapped onto a predetermined bit in the modulation symbol.

In this case, each of the plurality of bit groups may be formed of Mnumber of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc)and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Here,Q_(ldpc) is a cyclic shift parameter value regarding columns in a columngroup of an information word submatrix of a parity check matrix,N_(ldpc) is a length of an LDPC codeword, and K_(ldpc) is a length ofinformation word bits of an LDPC codeword.

Meanwhile, operation S1420 may include interleaving parity bits of theLDPC codeword, dividing the parity-interleaved LDPC codeword by aplurality of bit groups and rearranging the order of the plurality ofbit groups in bit group wise, and interleaving the plurality of bitgroups the order of which is rearranged.

The order of the plurality of bit groups may be rearranged in bit groupwise based on above-described Equation 21.

Meanwhile, π(j) in Equation 21 may be determined based on at least oneof a length of an LDPC codeword, a modulation method, and a code rate.

For example, when the LDPC codeword has the length of 16200, themodulation method is 16-QAM, and the code rate is 5/15, π(j) may bedefined as in Table 15.

Meanwhile, at S1420, dividing the LDPC codeword into the plurality ofbit groups, rearranging the order of the plurality of bit groups in bitgroup wise, and interleaving the plurality of bit groups of which theorder is rearranged are included.

However, this is merely exemplary, and π(j) may be defined as Tables15-27 described above.

The interleaving the plurality of bit groups may include: writing theplurality of bit groups in each of a plurality of columns in bit groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bit groupwise in a row direction.

In addition, the interleaving the plurality of bit groups may include:serially write, in the plurality of columns, at least some bit groupswhich are writable in the plurality of columns in bit group wise fromamong the plurality of bit groups, and then dividing and writing theother bit groups in an area which remains after the at least some bitgroups are written in the plurality of columns in bit group wise.

FIG. 39 is a block diagram illustrating a configuration of a receivingapparatus according to an exemplary embodiment.

Referring to FIG. 39 , a receiving apparatus 3800 may comprise acontroller 3810, an RF receiver 3820, a demodulator 3830 and a serviceregenerator 3840.

The controller 3810 determines an RF channel and a PLP through which aselected service is transmitted. The RF channel may be identified by acenter frequency and a bandwidth, and the PLP may be identified by itsPLP ID. A specific service may be transmitted through at least one PLPincluded in at least one RF channel, for each component constituting thespecific service. Hereinafter, for the sake of convenience ofexplanation, it is assumed that all of data needed to play back oneservice is transmitted as one PLP which is transmitted through one RFchannel. In other words, a service has only one data obtaining path toreproduce the service, and the data obtaining path is identified by anRF channel and a PLP.

The RF receiver 3820 detects an RF signal from an RF channel selected bya controller 3810 and delivers OFDM symbols, which are extracted byperforming signal processing on the RF signal, to the demodulator 3830.Herein, the signal processing may include synchronization, channelestimation, equalization, etc. Information required for the signalprocessing may be a value predetermined by the receiving apparatus 3810and a transmitter according to use and implementation thereof andincluded in a predetermined OFDM symbol among the OFDM symbols and thentransmitted to the receiving apparatus.

The demodulator 3830 performs signal processing on the OFDM symbols,extracts user packet and delivers the user packet to a servicereproducer 3740, and the service reproducer 3840 uses the user packet toreproduce and then output a service selected by a user. Here, a formatof the user packet may differ depending on a service implementationmethod and may be, for example, a TS packet or a IPv4 packet.

FIG. 40 is a block diagram illustrating a demodulator according to anexemplary embodiment.

Referring to FIG. 40 , a demodulator 3830 may include a frame demapper3831, a BICM decoder 3832 for L1 signaling, a controller 3833, a BICMdecoder 3834 and an output handler 3835.

The frame demapper 3831 selects a plurality of OFDM cells constitutingan FEC block which belongs to a selected PLP in a frame including OFDMsymbols, based on control information from the controller 3833, andprovides the selected OFDM cells to the BICM decoder 3834. The framedemapper 3831 also selects a plurality of OFDM cells corresponding to atleast one FEC block which includes L1 signaling, and delivers theselected OFDM cells to the BICM decoder 3832 for L1 signaling.

The BICM decoder for L1 signaling 3832 performs signal processing on anOFDM cell corresponding to an FEC block which includes L1 signaling,extracts L1 signaling bits and delivers the L1 signaling bits to thecontroller 3833. In this case, the signal processing may include anoperation of extracting an LLR value for decoding an LDPC codeword and aprocess of using the extracted LLR value to decode the LDPC codeword.

The controller 3833 extracts an L1 signaling table from the L1 signalingbits and uses the L1 signaling table value to control operations of theframe demapper 3831, the BICM decoder 3834 and the output handler 3835.FIG. 40 illustrates that the BICM decoder 3832 for L1 signaling does notuse control information of the controller 3833. However, when the L1signaling has a layer structure similar to the layer structure of theabove described L1 pre signaling and L1 post signaling, it is obviousthat the BICM decoder 3832 for L1 signaling may be constituted by atleast one BICM decoding block, and operation of this BICM decoding blockand the frame demapper 3831 may be controlled by L1 signalinginformation of an upper layer.

The BICM decoder 3834 performs signal processing on the OFDM cellsconstituting FEC blocks which belong to a selected PLP to extract BBF(Baseband frame)s and delivers the BBFs to the output handler 3835. Inthis case, the signal processing may include an operation of extractingan LLR value for decoding an LDPC codeword and an operation of using theextracted LLR value to decode the LDPC codeword, which may be performedbased on control information output from the controller 3833.

The output handler 3835 performs signal processing on a BBF, extracts auser packet and delivers the extracted user packet to a servicereproducer 3840. In this case, the signal processing may be performedbased on control information output from the controller 3833.

According to an exemplary embodiment, the output handler 3835 comprisesa BBF handler (not shown) which extracts BBP (Baseband packet) from theBBF.

FIG. 41 is a flowchart provided to illustrate an operation of areceiving apparatus from a moment when a user selects a service untilthe selected service is reproduced, according to an exemplaryembodiment.

It is assumed that service information on all services selectable by auser are acquired at an initial scan (S4010) prior to the user's serviceselection (S4020). Service information may include information on a RFchannel and a PLP which transmits data required to reproduce a specificservice in a current receiving apparatus. As an example of the serviceinformation, program specific information/service information (PSI/SI)in an MPEG2-TS is available, and normally can be achieved through L2signaling and an upper-layer signaling.

In the initial scan (S4010), comprehensive information on a payload typeof PLPs which are transmitted to a specific frequency band. As anexample, there may be information on whether every PLP transmitted tothe frequency band includes a specific type of data.

When the user selects a service (S4020), the receiving apparatustransforms the selected service to a transmitting frequency and performsRF signaling detection (S4030). In the frequency transforming operation(S4020), the service information may be used.

When an RF signal is detected, the receiving apparatus performs an L1signaling extracting operation from the detected RF signal (S4050).Then, the receiving apparatus selects a PLP transmitting the selectedservice, based on the extracted L1 signaling, (S4060) and extracts a BBFfrom the selected PLP (S4070). In S4060, the service information may beused.

The operation to extract a BBF (S4070) may include an operation ofdemapping the transmitted frame and selecting OFDM cells included in aPLP, an operation of extracting an LLR value for LDPC coding/decodingfrom an OFDM cell, and an operation of decoding the LDPC codeword usingthe extracted LLR value.

The receiving apparatus, using header information of an extracted BBF,extracts a BBP from the BBF (S4080). The receiving apparatus also usesheader information of an extracted BBP to extract a user packet from theextracted BBP (S4090). The extracted user packet is used to reproducethe selected service (S4100). In the BBP extraction operation (S4080)and user packet extraction operation (S4090), L1 signaling informationextracted in the L1 signaling extraction operation may be used.

According to an exemplary embodiment, the L1 signaling informationincludes information on types of a user packet transmitted through acorresponding PLP, and information on an operation used to encapsulatethe user packet in a BBF. The foregoing information may be used in theuser packet extraction operation (S1480). Specifically, this informationmay be used in an operation of extracting the user packet which is areverse operation of encapsulation of the user packet in the BBF. Inthis case, process for extracting user packet from the BBP (restoringnull TS packet and inserting TS sync byte) is same as above description.

A non-transitory computer readable medium, which stores a program forperforming the above encoding and/or interleaving methods according tovarious exemplary embodiments in sequence, may be provided.

The non-transitory computer readable medium refers to a medium thatstores data semi-permanently rather than storing data for a very shorttime, such as a register, a cache, and a memory, and is readable by anapparatus. The above-described various applications or programs may bestored in a non-transitory computer readable medium such as a compactdisc (CD), a digital versatile disk (DVD), a hard disk, a Blu-ray disk,a universal serial bus (USB), a memory card, and a read only memory(ROM), and may be provided. Although a bus is not illustrated in theblock diagrams of the transmitter apparatus and the receiver apparatus,communication may be performed between each element of each apparatusvia the bus. In addition, each apparatus may further include a processorsuch as a central processing unit (CPU) or a microprocessor to performthe above-described various operations.

At least one of the components, elements or units represented by a blockin illustrating the above-described transmitting apparatus and receivingapparatus may be embodied as various numbers of hardware, softwareand/or firmware structures that execute respective functions describedabove, according to an exemplary embodiment. For example, at least oneof these components, elements or units may use a direct circuitstructure, such as a memory, processing, logic, a look-up table, etc.that may execute the respective functions through controls of one ormore microprocessors or other control apparatuses. Also, at least one ofthese components, elements or units may be specifically embodied by amodule, a program, or a part of code, which contains one or moreexecutable instructions for performing specified logic functions, andexecuted by one or more microprocessors or other control apparatuses.Also, at least one of these components, elements or units may furtherinclude a processor such as a CPU that performs the respectivefunctions, a microprocessor, or the like. Two or more of thesecomponents, elements or units may be combined into one single component,element or unit which performs all operations or functions of thecombined two or more components, elements of units. Also, at least partof functions of at least one of these components, elements or units maybe performed by another of these components, element or units. Further,although a bus is not illustrated in the above block diagrams,communication between the components, elements or units may be performedthrough the bus. Functional aspects of the above exemplary embodimentsmay be implemented in algorithms that execute on one or more processors.Furthermore, the components, elements or units represented by a block orprocessing steps may employ any number of related art techniques forelectronics configuration, signal processing and/or control, dataprocessing and the like.

The foregoing exemplary embodiments and advantages are merely exemplaryand are not to be construed as limiting the present inventive concept.The exemplary embodiments can be readily applied to other types ofapparatuses. Also, the description of the exemplary embodiments isintended to be illustrative, and not to limit the scope of the inventiveconcept, and many alternatives, modifications, and variations will beapparent to those skilled in the art.

What is claimed is:
 1. A transmitting method comprising: generating acodeword comprising information bits and parity bits, wherein the paritybits are generated by encoding the information bits based on a lowdensity parity check (LDPC) code, a code rate of the LDPC code being5/15 and a code length of the LDPC code being 16200 bits; splitting thecodeword into a plurality of bit groups; interleaving the plurality ofbit groups to provide an interleaved codeword; mapping bits of theinterleaved codeword to constellation points for 16-quadrature amplitudemodulation (QAM); and transmitting a signal carrying the constellationpoints, wherein the plurality of bit groups are interleaved based on afollowing equation:Y _(j) =X _(π(j)) for (0≤j<N _(group)), where X_(j) is a j^(th) bitgroup among the plurality of bit groups, Y_(j) is a j^(th) bit groupamong the interleaved plurality of bit groups, N_(group) is a number ofthe plurality of bit groups, and π(j) denotes an interleaving order forthe interleaving, and wherein the π(j) is represented as follows: theinterleaving order π(j) (0 ≤ j < 45) Code j  0  1  2  3  4  5  6  7  8 9 10 11 Rate 23 24 25 26 27 28 29 30 31 32 33 34 5/15 π(j)  3 33 39  238 29  0 10 25 17  7 21 13 12 28 26 43 30 14 16 23 24 15  5 Code j 12 1314 15 16 17 18 19 20 21 22 Rate 35 36 37 38 39 40 41 42 43 44 5/15 π(j)44 37  8 34 20  1  4 31 11 42 22 18  9 36  6 19 32 40 41 35 27 .


2. The transmitting method of claim 1, wherein each of the plurality ofbit groups comprises 360 bits.
 3. The transmitting method of claim 1,wherein the π(j) is determined based on at least one of the code length,a modulation method for the mapping, and the code rate.
 4. A receivingmethod comprising: demodulating a signal received from a transmittingapparatus to generate values based on 16-quadrature amplitude modulation(QAM); splitting the values into a plurality of groups; deinterleavingthe plurality of groups to provide deinterleaved values; and decodingthe deinterleaved values based on a low density parity check (LDPC)code, a code rate of the LDPC code being 5/15 and a code length of theLDPC code being 16200 bits, wherein the plurality of groups aredeinterleaved based on a following equation:Y _(π(j)) =X _((j)) for (0≤j<N _(group)), where X_(j) is a j^(th) groupamong the plurality of groups, Y_(j) is a j^(th) group among thedeinterleaved plurality of groups, N_(group) is a number of theplurality of groups, and π(j) denotes an interleaving order for thedeinterleaving, and wherein the π(j) is represented as follows: theinterleaving order π(j) (0 ≤ j < 45) Code j 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 5/15 π(j) 3 33 39 2 38 29 0 10 25 17 7 2144 37 8 34 20 1 4 31 11 42 22 13 12 28 26 43 30 14 16 23 24 15 5 18 9 366 19 32 40 41 35 27 .


5. The receiving method of claim 4, wherein each of the plurality ofgroups comprises 360 values.
 6. The receiving method of claim 4, whereinthe π(j) is determined based on at least one of the code length, amodulation method for mapping, and the code rate.